Suman Chalise
Roll No. 32014
EE 3rd year.
Signal processing Tasks and Factors to be considered:
1) Conversion of signal
CT
DT
Analog
Digital
Mathematical/ Theoretical
CT to DT: Sampling
Impulse Train Sampling
Mathematically it is hard to do sampling thus we perform Impulse Train Sampling.
In impulse we manipulate x(t) with impulse train s(t).
x(t)
y(t)=x(t)*s(t)
s(t)
X(j)
×
Y(j) = 1/2 *X (j)×S(j)
S(j)
-Convolution with impulse gives same function.
-Convolution with shifted impulse gives shifted function.
c , maximum practical frequency containing of signal.
s ,sampling frequency.
We can preserve the signal after sampling if c ≤ s / 2, s ≥ 2c. this is the Sampling
Theorem (Nyquist Criteria).
If s < 2c, then there is spectral corruption after sampling, this is known as Aliasing.
If there is aliasing, the original signal cannot be recovered from sampled signal.
Analytically Y (j) is given by,
+∞
Y(j)= 1/T  X [ j(-ks)]
-∞
H(j) = 1
for ≤ s/2
0 , otherwise
Y (j) × H (j) = X (j)
X (j): we are unsure of exact value of c.
First before sampling, we need to reduce the effective bandwidth of X (j) to maximum
s/2. This may reduce the signal corruption. This is called using the anti-aliasing filter.
Anti-aliasing filter is compulsory in every sampling system (ADC).
xD [n
ADC
x(t)
y(t)
s(t)
4-bit unsigned
Conversion
to digital
xD [n]
= {0,1,2,…..,15
Quantization noise
added.
y(t)
S/H
t
ADC is performed to scale the signal to fit into dynamic range of ADC.
Due to digital signal conversion there is quantization noise added.
Noise power =∆2 /12 ; ∆-step size (min.)
This is normally called minimum noise, if signal fits exactly to the dynamic range of ADC.
# Digital to Analog Conversion.
DAC
XD[n]
yr (t)
Digital
S/H waveform-(Sample and Hold waveform)
Comparison between Analog and Digital filters
Analog filter
In analog filter both inputs and outputs are
continuous-time signal.
Implementations of such filter are carried
out using passive components.
Analog filter operates in infinite frequencies
range.
Main disadvantages of this is, higher noise
sensitivity.
Digital
In digital filters both inputs and outputs are
discrete-time signals
This filter is implemented on digital
computer or DSP.
Here frequencies are limited to half of
sampling rate.
It requires additional A/D and D/A
converter.
2) Filtering
-Filtering is for noise and inference reduction.
-Selection
-Equalization
-Recovery
3) Modulation
AM
FM
PM
PWM
3) Multiplexing