Introduction to Maintainability Engineering (RME 484)
Homework Assignment #3
Digital Signal Processing (DSP), DSP -1 & DSP -2
Show all your work.
Student Name: ___________________________________
Date: ____________
Problem 1
Before digitizing the signal from a load sensor in a metal rolling mill, the signal is conditioned to
eliminate certain frequency components and amplified using a drift-free amplifier.
(a) State the type of filter (common name) necessary to eliminate frequencies above 50
Hz. State the approximate value of this filter setting.
(b) State the type of filter (common name) necessary to eliminate frequency components
below 0.5 Hz. State the approximate value of this filter setting.
(c) If the two filters specified in (a) and (b) above are used simultaneously, state the range
of frequencies passed by this device. What is this filter commonly called?
Problem 2
A thermocouple is used to measure the temperature of water flowing in a pipe. The probability
distribution of signal, x(t), acquired from this thermocouple is approximated by a Gaussian
(normal) density function as given below:
(𝒙 − 𝟏𝟒𝟎)𝟐
𝒑(𝒙) =
𝒆𝒙𝒑 (−
)
𝟓𝟎
√𝟓𝟎 𝝅
𝟏
The physical unit of temperature is deg F.
(a) Calculate the mean value (m) and standard deviation (σ) of the temperature signal.
Indicates the units of both parameters.
(b) At what value of x, the above p(x) attains its maximum value? Calculate this maximum
value of p(x).
RME484-HW#3-1
Problem 3
The maximum frequency content in an accelerometer signal used for monitoring vibration of a
large fan bearing is 512 Hz. What is the minimum frequency with which the signal must be
sampled to satisfy the Nyquist sampling criterion?
Problem 4
State two reasons that cause the coherence function between two signals X(t) and Y(t) in the
frequency domain to be less than unity.
Problem 5
A block of digitized data of length N = 4096 (= 212) points is processed using the fast Fourier
transform (FFT).
(a) What is the approximate number of arithmetic operations using FFT?
(b) How does the numerical value in (a) compare with the number of approximate arithmetic
operations required if the computation is performed using the traditional approach? State
this numerical value.
Problem 6
X(t) is a stationary random signal with mean value zero. State which of the following properties
of its autocorrelation function, Rxx(τ), are always true.
(a)
(b)
(c)
(d)
(e)
Rxx(τ) must be an even function of τ.
Rxx(τ) must be nonnegative.
Rxx(τ) has its largest value at τ = 0.
Rxx(τ) is always oscillatory as a function of τ.
The autocorrelation function, Rxx(τ), is a minimum at lag τ = 0.
RME484-HW#3-2