signal processing level 3

Question 1

advantages to digital implementation of signal processing

Answer 1

1 Signals and Systems are Stored in Digital Computers and
Transmitted in Digital Form.
2. DSP is stable and reliable in Contrast to Analogue components which drift with Temperature, Humidity, Time, Etc
. DSP can be used to process a number of signals simultaneously
(TDM)
4. Accuracy can be precisely controlled in contrast to analogue
Systems where Component Tolerances and Inaccuracies Are
Not Precisely Known.
5. More powerful DSP devices are becoming available at lower costs
Digital filters offer the following advantages:
➢Practical and cheap very low frequencies filters can be implemented
Analogue filters require large components.
➢Frequency response can be made to approach the ideal more closely
than analogue counterpart.
➢Adaptive filtering is readily achievable particularly with
Microcomputers & Microprocessors
➢Filters with linear phase characteristics are possible.

Question 2

Explain what is meant by a time invariant system.

Answer 2

Time invariance means that the system response remains unchanged
with the time of the excitation so
if x(t) gives y(t) then x(t-to) gives y(t-to)

Question 3

Distinguish between the impulse response and the unit step response of a linear time invariant system and give the relationship between the two responses.

Answer 3

The impulse response is the output of the system when the input is an impulse usually designated as h(t) while the unit response is the output of the system when the input is a unit step function.

d(t) gives h(t) while u(t) gives s(t)

The relationship between the impulse function and the unit step
function is as follows
d(t)=d(u(t))/dt or alternatively u(t) is the integral of d(t)
Since a derivative at the input gives a derivative at the output the impulse response can be found by taking the derivative of the unit step response and vice versa

Question 4

steps for convolution of x(t) and y(t)

Answer 4

1. Replace the independent variable with a dummy variable in both
   functions x(t) with y(t).
2. Time reverse one of the two functions e.g. x(-t)
3. Multiply the two functions x(-t).y(t)
   and find the area under the product. This gives the value of
   convolution at zero time shift
4. Add a delay with the independent variable
   x(t-t). For each delay multiple the two functions x(t-t).y(t) and find the area under the product and this gives the value of convolution at t which is the original time variable.
5. Repeat for all values of t until there are no common areas under the product.
6. Convolution of two signals of duration T1 and T2 is equal to T1+T2

Question 5

how do you tell if a signal is time invariant

Answer 5

This can be proven as follows;
A delayed input x[n-no] gives an output, if delaying y[n], y[n-no] gives the same then it is time invariant.
The system is time variant if the input is multiplied by n which is the independent variable.

Question 6

how do you tell if a signal is linear

Question 7

what is causalilty and how can a signal be causal

Answer 7

h(t) = 0 for t<0
h[n]= 0 for n<0

Question 8

name 5 practical applications of signal processing

Answer 8

1. Signal Detection from Noise: extraction of voice signal of a pilot from noisy engine background,
   image enhancement of a satellite transmission, and quality improvement of music obtained from
   old recordings.
2. Forecasting: Given past history values a computer programme can be written to predict future
   values. For example, stock market data and weather forecast.
3. Waveform analysis: finding the frequency components in a signal, such as speech or sound or
   the resonances.
4. Waveform synthesis: such as synthesizing music or speech.
5. System characterization: Finding the frequency response of the auditory system, or the
   oscillations of a damped system following application of a force and the resonances of a vibrating
   system.
6. System Modification: regulating the system response such as controlling the temperature of a
   burner or controlling the speed of a car under ‘cruise control’.
7. Filtering: for example, elimination of mains hum from an ECG Signal using a notch filter at
   60Hz

Question 9

what is the power of an energy signal

Answer 9

0

Question 10

what is the energy of a power signal

Answer 10

infinite

Question 11

give an example of a non linear system

Answer 11

A multiplier is a nonlinear system where the output has new
frequencies.
Similarly a squarer is a nonlinear system.

Question 12

Overall impulse response of two linear
time invariant systems assembled (i) in cascade, (ii) in parallel

Answer 12

ℎ(𝑡)= ℎ1 (𝑡) ∗ ℎ2(𝑡) Cascade systems
ℎ(𝑡) = ℎ1(𝑡) + ℎ2(𝑡) Parallel systems