DTMF Generator using IIR Filter
with the chipKIT™ Pro MX7
Revision: April 12, 2015
Richard W. Wall
1300 NE Henley Court, Suite 3
Pullman, WA 99163
(509) 334 6306 Voice | (509) 334 6300 Fax
Project 14b: IIR DTMF Digital Generators
Table of Contents
Project 14b: IIR DTMF Digital Generators ......................................................................................... 1
Table of Contents .................................................................................................................................. 1
Purpose ..................................................................................................................................................... 2
Minimum Knowledge and Programming Skills ......................................................................................... 2
Equipment List........................................................................................................................................... 2
Software Resources ................................................................................................................................... 2
References ................................................................................................................................................. 2
DTMF ......................................................................................................................................................... 3
Introduction to Digital Signal Processing .................................................................................................. 5
Digital Filter Fundamentals ................................................................................................................... 5
The Z-Plane Unit Circle .......................................................................................................................... 6
An IIR Digital Oscillator.......................................................................................................................... 7
C Code for Dual Tone to Key conversion: ................................................................................................. 9
16 Button Keypad................................................................................................................................ 10
Digital Oscillator .................................................................................................................................. 11
Analog Output Filtering........................................................................................................................... 14
Code Performance ................................................................................................................................... 16
Final Remarks .......................................................................................................................................... 20
APPRNDIX I - Hardware Configuration ........................................................................................................ 22
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Purpose
The purpose of this reference design is to present a method for using a PIC32 microcontroller to
generate DTMF tones using digital filter technology. The technique that will be demonstrated in this
reference design uses the power of digital signal processing that requires only 64 bytes of memory and a
minimal amount of processor computation. The performance of this approach clearly demonstrates that
generating multiple tone signals requires a minimum of microprocessor resources.
Minimum Knowledge and Programming Skills
1. Knowledge of C or C++ programming
2. Working knowledge of MPLAB® X IDE
3. LCD Interface (Optional)
4. Understanding of Finite Impulse Response Filters
5. DTMF tones
Equipment List
1. chipKITTM Pro MX7 processor board with USB cable
2. Pmod-DA2 Dual Channel D to A converter
3. PmodKYPD 16 Button Keypad
4.
PmodSTEP Stepper Motor Driver module (Used for performance timing)
5. Character LCD (optional)
6. Logic analyzer, or oscilloscope (Suggestion - Digilent Analog Discovery)
Software Resources
1. MPLAB® X Integrated Development Environment (IDE)\
2. MPLAB® XC32 C/C++ Compiler
3. XC32® C/C++ Compiler Users Guide
References
1. chipKITTM Pro MX7 Board Reference Manual
2. C Programming Reference
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3. PIC32 Family Reference Manual, Timers Section 14:
http://ww1.microchip.com/downloads/en/DeviceDoc/61105E.pdf
4. Web Based DTMF Signal Generator
5. “A Discrete Fourier Transform Based Digital DTMF Detection Algorithm”,
http://www.rootsecure.net/content/downloads/pdf/paper_dtmf.pdf
6.
“Specification of Dual Tone Multi-Frequency (DTMF) Transmitters and Receivers”
http://www.etsi.org/deliver/etsi_es/201200_201299/20123502/01.01.01_60/es_20123502v010
101p.pdf
7. Steven W. Smith, The Scientist and Engineer’s Guide to Digital Signal Processing
DTMF
Touch tone dialing was introduced by AT&T for telephones in 1963 as a replacement for rotary dialsi.
The primary advantage of touch tone dialing over rotary dialing is that the dialing information can be
carried in the audio band where as the dialing information for rotary dialing is DC. The rotary phones
(circa 1891-present day) created pulses in the voltage supplied by the telephone exchange to power the
telephone. Rotary dials are mechanical devices that use a cam to actuate a mechanical switch. Over time
the mechanics of the rotary dial would break or begin to operate so slowly that the pulses could no
longer be accurately decoded. Conventional touch tone operated telephones have 12 keys: 0 through 9
as well as the “*” and “#” keys. The full implementation of the touch tone key pad as shown in Figure 1
contains 16 keys. The additional four keys are designated A through D. Some phone systems use the
additional keys for phone system management and control.
Figure 1. Key organization for 16 Key touch tone pad ii
Touch tone phones generate a multi tone signal containing the combination of two signals at set
frequencies hence the designation of DTMF for the dual tones multiple frequencies employed. As
illustrated in Table I, there are four row frequencies (697 Hz, 770 Hz, 852 Hz, and 941 Hz) and four
column frequencies (1209 Hz, 1336 Hz, 1477 Hz, and 1633 Hz). Whenever a key is pressed, the signal is
generated that consists of the two frequencies specified by the key’s row and column. DTMF standards
specify that the frequencies of the eight DTMF tones be accurate to within 1.8%. This tolerance results
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in a tone band width of 25Hz based on the row one frequency to 59 Hz for the column four. This has
ramifications when designing a digital filter to identify the tone pairs when a key is pressed.
Table I. DTMF keypad frequencies
1209 Hz 1336 Hz 1477 Hz 1633 Hz
697 Hz
1
2
3
A
770 Hz
4
5
6
B
852 Hz
7
8
9
C
941 Hz
*
0
#
D
DTMF signals in the form of wave files can be generated using a web-based audio generator. However,
this technique for generating DTMF tones requires 16 memory arrays each containing a minimum of 12
integers or a total of 384 bytes of memory. Figure 2 shows the series of outputs that are required to
generate the minimum and maximum frequency DTMF tones as well as the sum that would be needed
to generate the tones for the “D” key. The series of 12 outputs needs to be repeated generated at an
8KHz rate. Observe that initial output of each series is zero. This is a result of synthesizing the series
using a sine function. When repeating this sequence of output, this initial output may not
mathematically follow the last output in the series. This discontinuity both spreads the spectrum of the
tone frequencies and well as generating harmonic as illustrated in Figure 3 and Figure 4. Depending on
the amount of frequency spreading generated, the resulting signal can exceed the DTMF specification
provided above.
8 KHz DTMF Tone Samples
Amplitude
2
1
0
1
2
0
5
10
Sample
ROW 1 Tone
COL 4 Tone
Sum of Tones
Figure 2. Sample plots for the lowest and highest DTMF tone frequencies
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Spectrum of Table Driven output ofr ROW 1 Tone
Magnitude
0.05
0.04
0.03
0.02
0.01
0
660
680
700
720
740
Frequency - Hz
DFT of ROW 1
Figure 3. Frequency spectrum of Row 1 tone generated with a table
Spectrum of Table Driven Output for Column 4 Tone
Magnitude
0.05
0.04
0.03
0.02
0.01
0
3
1.610
3
1.6510
3
1.710
3
1.7510
3
1.810
Frequency - Hz
DFT of COL 4
Figure 4. Frequency spectrum of Column 4 tone generated with a table
Introduction to Digital Signal Processing
Digital Filter Fundamentals
Digital filters are a subset of a technology known as digital signal processing (DSP) that data back to the
1960’s. The digital filter is a computer algorithm that process data sets or discrete time sampled data to
isolate information in one frequency range from signals or noise in other frequency ranges. Digital filters
function in a similar manner to analog filters that are electronic circuits designed using resistors,
capacitors, inductors, and operational amplifiers. Although it is beyond the scope of this tutorial to
present a complete treatment of digital filter design, a brief introduction is provided to assist the reader
in understanding the concept that is used to generate the digital oscillators.
Figure 1 is a block diagram representing the components of a typical DSP application. For the DSP
algorithm to function correctly, the frequency range of the input to analog filter must be limited to being
no greater than half the rate that the input signal is sampled. This sampling rate is referred to as the
Nyquist rate. An analog filter is commonly used to preprocess the input signal so that signal frequencies
higher than the Nyquist rate are greatly attenuated.
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PIC32 Microprocessor
Analog
Input
Analog Antialiasing
Filter
Sample and
Hold
Analog to
Digital
Converter
(ADC)
DSP
Algorithm
(Software)
Digital to
Analog
Converter
(DAC)
Analog
Output Filter
Analog
Output
Figure 5. Microprocessor Digital Signal Processing block diagram
One mathematical representation of a digital filter algorithm is expressed a ratio of the output to the
inputs that are expressed by two polynomials in z inverse as shown in Equations 1. The term z-1
represents a delay of one sample period while the ai and bi coefficients are uniquely determined based
on the requirements of the digital filter. Procedures for determining these polynomial coefficients will
be addressed below.
Equation 1.
Equating X(z)*z-i to x(n-i) and Y(z)*z-k to y(n-k), Equation 1 can be rewritten as shown in Equation 2 which
is the general form of a recursive difference equation. The expression x(n-i) represents the input sample
that occurred “i” samples earlier.
Equation 2.
Equation 2 is a recursive equation that requires present and past inputs as well as past outputs.
Recursive equations are referred to as an infinite impulse response (IIR) filters because the feedback of
past outputs gives the filter infinite memory.
If a filter is generated that results in all coefficient ak = 0 for k > 0, then the filter has no memory and is
referred to as a finite impulse response (FIR) filters. The outputs of FIR filters are a function of the
coefficients that multiple present and past inputs. Once an input exceeds the number of delays equal to
the order of the numerator polynomial in Equation 2, the input is forgotten hence inputs have finite
persistence.
The Z-Plane Unit Circle
It will become obvious in the reference design to need to understand the z-plane representation of
digital filters. Roots of the numeration of the polynomial expressed in Equation 1 are called “zeros”.
Roots of the denominator polynomial are referred to as poles.  Figure 6 illustrates the poles (denoted as
a blue triangle) and zeros (denoted as red dots) for a digital filter plotted on the z-plane. Since the digit
filter design process generates a unique polynomial, the placement of the poles and zeros in the z-plane
are equally unique. Zeros on the unit circle will cause the filter to output a zero amplitude signal when
excited at the frequency corresponding to the angle . Poles on the unit circle cause the polynomial
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denominator to equal zero hence the output of the filter will be infinite when excited at the frequency
corresponding to the angle from the real axis. Poles outside the units circle indicate that the filter is
unstable and the amplitude of the oscillations will increase toward infinity. Poles just inside the unit
circle will cause the filter to oscillate however the amplitude is bounded (fixed maximum). We will take
advantage of this characteristic to make the eight oscillators needed for the DTMF tones.
Chebyshevy II Filter Response
Z Plane Unit Circle
0
1
ej1

=p,
z=1 0
 20
=0,
z=1
 40
 60
 0.5
1
1
Amplitude
Imaginary
0.5
 0.5
0
0.5
1
Real
Figure 6. Poles and zeros plotted on the z-plane
 80
0
1
2
3
Frequency - Hz
Figure 7. Digital filter frequency response
Note that poles and zeros that do not lie on the real axis exist in complex conjugate pairs. The effect of
zeros on the filter response can be clearly noted on Figure 7. The z-plane frequency, , relates to the
real-world signal frequency by noting that  = p for f = the Nyquist rate which is half of the sampling
rate in samples per second.
An IIR Digital Oscillator
As discussed above, there are eight unique DTMF frequencies: one for each of the button rows and one
for each of the button columns. From the previous discussion we can compute the eight complex
conjugate pairs associated with the eight DTMF frequencies as i = Fi/Fs for i = 1 through 8 and Fs is the
rate that the new outputs are generated. Table I lists the four row and the four column tone
frequencies. Table II lists the normalized frequencies in radians for the eight tones that are computed by
dividing by the sampling frequency.
Digital signal processing theory states that of the denominator polynomial (poles) that lie on the unit
circle results in filters that are not, by definition roots, stable. However, if the filter poles are exactly on
the unit circle oscillations are sustained but neither grows nor diminishes in amplitude. The filters that
we are designing to be used as oscillators make use of this characteristic. The pairs of complex conjugate
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poles presented in Table III that lie on the unit circle are generated using Equation 3. The filter gain for
each oscillator, also listed in Table II, are scale factors needed to make the peak amplitudes equal to ±1.
Figure 8 shows the eight pairs of complex conjugate pole pairs are plotted on a z-plane graph.
Equation 3
Table II. Normalized oscillator frequencies
2 p Fr1
Fs
2 p Fr2
R2 =
Fs
2 p Fr3
R3 =
Fs
2 p Fr4
R4 =
Fs
R1 =
= 0.547
= 0.605
= 0.669
= 0.739
2 p Fc1
Fs
2 p Fc2
C2 =
Fs
2 p Fc3
C3 =
Fs
2 p Fc4
C4 =
Fs
C1 =
= 0.95
= 1.049
= 1.16
= 1.283
Table III. Complex conjugate pole pairs and transfer function gain for the row and column tones
Row frequency poles pairs

e
PR1 = 
 e


e
PR2 = 
 e


e
PR3 = 
 e


e
PR4 = 
 e


 0.854  0.52i 
 =

 1  R1 
 0.854  0.52i 

 1  R2 
  0.823  0.569i 
 =

 1  R2 
 0.823  0.569i 

 1  R3 
  0.784  0.62i 
 =

 1  R3 
 0.784  0.62i 

 1  R1

 0.739  0.674i 
 =

 1  R4 
 0.739  0.674i 

Column frequency poles pairs
GR1=0.520

e
PC1 = 
 e

GR2=0.569
PC2 = 
GR3=0.620
 1  R4
GR4=0.676

e
 e


e
PC3 = 
 e


e
PC4 = 
 e


 0.582  0.813i 
 =

 1  C1 
 0.582  0.813i 

 1 C1

 0.498  0.867i 
 =

 1  C2 
 0.498  0.867i 

 1 C3 
  0.399  0.917i 
 =

 1  C3 
 0.399  0.917i 

 1 C4 
  0.284  0.959i 
 =

 1  C4 
 0.284  0.959i 

GC14=0.813
 1 C2
GC2=0.871
GC3=0.917
GC4=0.959
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Z Plane Unit Circle for the 8 DTMF Oscillators
1.1
=jp
0.733
Imaginary
0.367
=p,
0
z=1
=0,
z=1
 0.367
 0.733
 1.1
 1.1
=jp
 0.733
 0.367
0
0.367
0.733
1.1
Real
Figure 8. Pole-zero plot for the 8 DTMF oscillators
The required eight oscillator transfer functions are computed using Equation 4. Since the input is a unit
impulse and only exists for the computation of the y[0] output which is set for as the digital filter initial
condition.
–
Equation 4
Each of the eight digital oscillator filters have unique values for the coefficient a1 and Gi.
Equation 5
To generate the two tones associated with a particular key pressed, two oscillating filters are activated
and the output added together before being sent to the digital to analog converter.
C Code for Dual Tone to Key conversion:
Listing 1 shows the code for the function main. After initializing the hardware, the keypad is
continuously polled using “read_keypad” to determine is any key is pressed. The function, “start_tones”
is called that provides the row and column of the key that is pressed. If “NO_KEY” is detected, row and
column zero are sent to “start_tones”. This turns off all oscillators. Since the “start_tones” function
initializes the digital filters, this function is only called when a new key is pressed or when a key is let up.
Listing 1.
int main(void)
{
int row = 0, col = 0;
setup_hardware();
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while(1)
{
key1 = read_keypad(&row, &col); /* poll key pad */
if(key1 != key2)
/* Check for change of key state */
{
key2 = key1;
if(key1 == NO_KEY)
start_tones(0, 0);
/* Stop oscillations *
else
start_tones(row, col); /* Start tone generation */
}
}
return (EXIT_FAILURE);
}
16 Button Keypad
A Digilent Pmod-KYPD 16-key keypad is used to indicate which of the 16 tone pairs is to be generated. As
shown in Figure 9 the ‘#’ and ‘*’ keys are not represented on the keypad. The code for this reference
designs associates the conventional ‘*’ with the keypad ‘F’ key and the conventional ‘#’ key with the
keypad ‘E’ key. The Pmod-KYPD 16 provides four inputs and four outputs. The keys are scanned using a
walking zero pattern for the column outputs and reading the row inputs. Since the Pmod connectors on
the chipKIT Pro MX7 are not connected consecutively to the PIC32 IO port pins, individual IO must be
managed in a bit-bang fashion. CAUTION: Do not attempt to use the JD connector on the chipKIT Pro
MX7 for the keypad interface as two of the pins also connect to the RS232 FTDI IC on the processor
board. This reference design uses the chipKIT Pro MX7 JF port. The driver code for the keypad interface
is provided in files “keypad.c” and “keypad.h”. The function, “keypad_init”, must be call prior to calling
the function “read_keypad” which when called will return values in the row and column variable
associated with a pressed key. This function returns a “NO_KEY” or one of the key identifiers.
The “read_keypad” function also displays the key that is pressed on the LCD.
Figure 9. Digilent Pmod-KYPD 16 button Keypad
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Digital Oscillator
The Table IV lists the functions in the “dtmf_gen.c” file and briefly describes their functionality.
Following Table IV, the code for these functions is included to illustrate the simplicity of operation. All
functions listed as static are private (exclusive) to outer functions in this file.
The Timer 1 ISR is set to generate an interrupt each 0.125ms which generates the 8KHz sample rate. The
call to generate a new analog output is disabled only when the filter coefficients change. When there is
no button pressed on the 16 button keypad, the row and column tone filter coefficients are set to zero.
The analog output is offset to one half of the the maximum output. If the output is to drive a speaker, a
DC blocking capacitor must be used.
Constant definitions are provided by the support header file ”dtmf_gen.h”
Table IV. dtmf_gen.c functions
Listing
Number
1
2
3
4
5
6
Function name
void start_tones(int row, int col);
static void select_filters(int row, int col);
static void gen_tones(void);
static void DA2(WORD CH1, WORD CH2);
static void pwm_analog(int ana);
void __ISR(_TIMER_1_VECTOR, IPL2SOFT)
Timer1Handler(void)
Description
Selects the filter coefficients and starts oscillation
Selects filter coefficients
IIR filter that generates the analog outputs
Analog output using PmodDA2
Analog output using PWM (Timer 2)
Analog output timer (Timer 1)
Listing 1
/* Select oscillator constants according to row and column number */
static void select_filter(int row, int col)
{
switch(row)
{
case 1:
row_filter.a0 = filt_r1[0];
row_filter.a1 = filt_r1[1];
row_filter.a2 = filt_r1[2];
break;
case 2:
row_filter.a0 = filt_r2[0];
row_filter.a1 = filt_r2[1];
row_filter.a2 = filt_r2[2];
break;
case 3:
row_filter.a0 = filt_r3[0];
row_filter.a1 = filt_r3[1];
row_filter.a2 = filt_r3[2];
break;
case 4:
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row_filter.a0
row_filter.a1
row_filter.a2
break;
default:
row_filter.a0
row_filter.a1
row_filter.a2
break;
}
switch(col)
{
case 1:
col_filter.a0
col_filter.a1
col_filter.a2
break;
case 2:
col_filter.a0
col_filter.a1
col_filter.a2
break;
case 3:
col_filter.a0
col_filter.a1
col_filter.a2
break;
case 4:
col_filter.a0
col_filter.a1
col_filter.a2
break;
default:
col_filter.a0
col_filter.a1
col_filter.a2
break;
}
= filt_r4[0];
= filt_r4[1];
= filt_r4[2];
= 0;
= 0;
= 0;
= filt_c1[0];
= filt_c1[1];
= filt_c1[2];
= filt_c2[0];
= filt_c2[1];
= filt_c2[2];
= filt_c3[0];
= filt_c3[1];
= filt_c3[2];
= filt_c4[0];
= filt_c4[1];
= filt_c4[2];
= 0;
= 0;
= 0;
}
Listing 2
/* ------------------- Set Oscillator frequency ------------------------ */
void start_tones(int row, int col)
{
tones_active = FALSE;
/* Disable Timer ISR oscillator */
select_filter(row, col);
/* Set filter coefficients */
x[0] = row_filter.a1;
x[1] = 0;
x[2] = 0;
/* Initialize Row oscillator filter */
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y[0] = col_filter.a1;
y[1] = 0;
y[2] = 0;
/* Initialize Row oscillator filter */
tones_active = TRUE;
/* Enable Timer ISR oscillator */
}
Listing 3
/* --------------- Tone generator IIR Filter code ------------ */
static void gen_tones(void)
{
int ch1, ch2 = 2048;
/* Set Channel 2 for DC output */
/* Row oscillator IIR filter */
x[2] = x[1];
/* Shift row channel outputs and compute new output */
x[1] = x[0];
x[0] = (row_filter.a1 * x[1] + row_filter.a2 * x[2]) >> 8;
/* Column oscillator IIR filter */
y[2] = y[1];
/* Shift column channel outputs and compute new output */
y[1] = y[0];
y[0] = (col_filter.a1 * y[1] + col_filter.a2 * y[2]) >> 8;
/* Sum and add offset to signal */
ch1 = (y[0] + x[0]) + 2048;
if(ch1 <
ch1
if(ch1 >
ch1
0)
= 0;
4097)
= 4097;
pwm_analog(ch1 >> 2);
DA2(ch1, ch2);
/* Send scaled ch1 output to PWM */
/* Send ch1 and ch2 output to DAC */
}
Listing 4
/* -------------------------- Output to PmodDA2 ---------------------------- */
/* Bit bang SPI because it outputs to two analog channels simultaneously */
static void DA2(WORD CH1, WORD CH2)
{
int i;
PULSE_SCLK();
/* Reset DAC */
PULSE_SYNC();
for(i = 15; i >= 0; i--)
/* Shift out data bits MSB first */
{
CHAN_A = (CH1 >> i) & 0x01;
CHAN_B = (CH2 >> i) & 0x01;
PULSE_SCLK();
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}
PULSE_SCLK();
/* Finalize SPI transfer */
}
Listing 5
/* --------------------------- PWM update ------------------------------ */
static void pwm_analog(int ana)
{
SetDCOC3PWM(ana);
/* Set PWM ratio */
}
Listing 6
/* ------------------ Time 1 Interrupt Service Routine ----------------- */
void __ISR(_TIMER_1_VECTOR, IPL2SOFT) Timer1Handler(void)
{
if(tones_active == TRUE)
/* Call IIR filter only if turned on */
gen_tones()
INTClearFlag( INT_T1 );
/* Clear the Timer interrupt flag */
}
Analog Output Filtering
Figure 10 show a captured waveform of the output for the PWM and DAC. The PWM carrier frequency
and the DAC update rate are both 8KHz. Figure 11 is a similar waveform capture showing the PWM
output after being filtered with a simple RC low-pass filter. Note that the peak to peak filtered PWM
output is only 0.2V. In most applications, an analog amplifier would be necessary thus permitting the
implementation on a third order filter requiring only three resistors, three capacitors and a dual
operations amplifier IC1,2.
Figure 13 shows a simulated output when both the DAC and the PWM outputs are filtered with a third
order Butterworth low-pass analog filter with a cutoff frequency set for 1700Hz. This filter has a
frequency response as shown in Figure 12.
1
http://www.analog.com/library/analogDialogue/archives/43-09/EDCh%208%20filter.pdf
2
http://www.maximintegrated.com/en/app-notes/index.mvp/id/1795
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DTMF Tone Generation
TM
with the ChipKIT Pro MX7™
Figure 10. DAC and PWM Output Signal
st
Figure 11. DAC and RC (100k / 0.33uF) 1 order filtered PWM output
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DTMF Tone Generation
TM
with the ChipKIT Pro MX7™
3rd Order Butterw orth Analog Filter Frequency Response
Gain - db
0
 10
 20
0
3
3
110
210
3
310
3
410
Frequency - Hz
Figure 12. Output 3rd order filter frequency response
Analog Filtered DAC and PWM outputs
Amplitude
3
2
1
0
0
2
4
Time - ms
Filtered DAC
Filtered PWM
Figure 13. High order analog filtered DAC and PWM outputs
Code Performance
The frequency accuracy signals generated by the IIR oscillator algorithm are shown in Table V. The
measurements were made using the frequency output of a Fluke 867B Graphical Multimeter. The results
show that the worse frequency case is less than 0.18% making the accuracy greater than 99%. The
measured error is 10 times less than the DTMF standard requires.
Table V. Measured Tone Frequency Errors
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DTMF Tone Generation
TM
with the ChipKIT Pro MX7™
Row
1
2
3
4
Column
1
2
3
4
Standard
697
770
852
941
IIR Measured
697.48
770.37
853.50
941.78
% Error
0.07%
0.05%
0.18%
0.08%
1209
1336
1477
1633
1208.4
1335.5
1477.5
1630.6
-0.05%
-0.03%
0.03%
-0.14%
Table VI provides a performance measure for this implementation of the DTMF signal. Although the
PIC32 processor has software floating point capability, the signal generating IIR filter shown in Listing 3
uses integer mathematics for improved speed performance. All filter constants are scaled by 256. For
example, the row 1 filter constants are defined by the declaration:
int filt_r1[3] = {K_R1, 437, 256}; /* R1 */
K_R1 is the scale numerator coefficient listed in Table IV as GR1. The second element in the array is the
scaled a1 coefficient as described by Equation 5. The last element in the coefficient array is the scaled
value of 1 used for the a2 coefficient.
The actual IIR filter is implemented with the line of C code shown below. Since the scale factor is a
power of 2, the multiplication and division by 256 is implemented with right and left binary shift
operations both of which require only 150ns to implement.
x[0] = (row_filter.a1 * x[1] - row_filter.a2 * x[2]) >> 8;
/* >> 8 = divide by 256 */
The run-time execution performance reported in Table 6 shows that the bit-banged SPI output is by far
the slowest executing process. Figure 14 and Figure 15 show the timing waveforms for a DAC update
cycle. The trace labeled LEDA is the duration of time needed to execute the program code of Listing 3
for the two IIR filters.
Table VI. Task code execution timing
Task
Sample Rate
Interrupt latency
IIR Filters
SPI Analog Output
Execution Time
8KHz
1.03 s
1.03 s
9.94 s
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DTMF Tone Generation
TM
with the ChipKIT Pro MX7™
Figure 14. Timing of the DTMF decoder program.
Figure 15. Expanded view of the time required for decoding and LCD update.
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DTMF Tone Generation
TM
with the ChipKIT Pro MX7™
Figure 16. DAC output for two-tone generation when sampled at 8KHz
page 19 of 22
DTMF Tone Generation
TM
with the ChipKIT Pro MX7™
Figure 17. Fourier series of a digitally generated two DTMF tones showing the sidebands create by
modulation due to sampling when using a DAC.
Final Remarks
The IIR oscillator provides very accurate frequency signal generation with a minimal amount of
computational burden. The time to compute an analog output is a faster than the bit-banged SPI DAC
interface by a factor of 10. This can be significantly reduced by using a different DAC device.
page 20 of 22
DTMF Tone Generation
TM
with the ChipKIT Pro MX7™
The tradeoff between using a PWM output and a DAC depends the degree of analog output filtering.
The PWM requires significantly more analog electronics to achieve that same degree of digital
modulation rejection as a DAC output. The DAC used in this design requires three IO pins whereas the
PWM requires only one.
A discontinued Digilent PmodAMP1 was used for this project. This module had the advantage of using a
DC blocking capacitor to remove the DAC and PWM DC bias. Future designs will consider using the
PmodAMP3 which combines a power amplifier with a stereo DAC using an I2S serial interface.
page 21 of 22
DTMF Tone Generation
TM
with the ChipKIT Pro MX7™
APPRNDIX I - Hardware Configuration
chipKIT PRO MX7
PC
PModCLP
PMP Ctrl Bus –JC
Pins7 , 8 , and 9
2 X 16
Character
LCD
DEBUG USB
(5 V PWR)
PG.12
PG.13
PG.14
PG.15
PModKYPD
JF
RD9 – JD1
RD0 – JD2
RC4 – JD3
RC10 – JD4
GND – JD5
3.3V – JD6
BTN1
BTN2
BTN3
1 - SYNC
2 -DINA
3 - DINB
4 - SCLK
6 - Gnd
7 - Vcc
VOUTA -1
N/C - 3
VOUTA -2
N/C - 4
Gnd - 6
Vcc - 7
1-LEFT
2-N/C
3-RIGHT
4-N/C
5-GND
6-Vcc
PmodAMP1
LED1
LED2
LED3
LED4
Pmod-DAC2
MPLAB
IDE
PMP Data Bus- JB
LEFT
DAC Audio
GND
Output
RIGHT
PG.6
PG.7
PA.0
RD2 – JD8
OC3
100K
33nF
PWM Audio
Output
GND – JD11
i
ii
http://en.wikipedia.org/wiki/Rotary_dial
http://en.wikipedia.org/wiki/Dual-tone_multi-frequency_signaling#.23.2C_.2A.2C_A.2C_B.2C_C.2C_and_D
page 22 of 22