1. A signal is sampled at the Nyquist rate. Will we be able to reconstruct the original signal from a sampled signal?
Ans. No, when a signal is sampled at Nyquist rate then, to reconstruct the original, signal from sampled signal faithfully, an ideal LPF is required which in real life is impossible to construct.
2. Suppose a quantized signal x(t) is given to you. Are you able to construct the original signal x(t) from x(t0)?
Ans. No, since quantizer is a non-invertible system so we can not construct the original signal from quantized signal. While quantization there is an error associated with the system as sampled value and quantized value are different.
3. What is the similarity between the Laplace transform and Z-transform? Explain.
Ans. Z-transform is the discrete time counterpart of Laplace transform with negative real axis mapped within the unit circle, jω -axis mapped on the unit circle and right half mapped on outside unit circle.
4. What is dithering?
Ans. Dithering is a common technique in which noise is deliberately added to the slowly varying signal so as to improve the digitization of such kind of signals. Dither is an intentionally applied form of noise used to randomize quantization error, preventing large-scale patterns such as colour banding in images. Dither is routinely used in the processing of both digital audio and video data.
5. Explain the difference between DTFT and DFT.
Ans. In DTFT the discrete signal is aperiodic so the frequency domain signal is periodic and continuous whereas, in DFT, the discrete signal is periodic and discrete.
6. What do you mean by sinusoidal fidelity? Explain.
Ans. If the input to a linear system is a sinusoidal wave, the output will also be a sinusoidal wave, and at exactly the same frequency as the input. Only the amplitude and phase can be different.
7. Why windowing is necessary for a sampled signal? Explain.
Ans. When a signal is sampled and FFT is performed directly then the first side lobe is only 14 dB less than the main lobe i.e. the SNR is very poor. Windowing of sampled signal is done to improve the ratio between the main lobe and the first side-lobe.
8. Which filter is having better frequency dynamic range Analog and digital filter?
Ans. Analog signal is having better frequency dynamic range. An op-amp filter can handle signal as slow as 0.01 Hz to 100 kHz. In digital filter minimum sampling frequency required is 200 kHz and to sample one cycle of 0.01 Hz it requires.
9. An impulse represents which type of filter? Explain it.
Ans. All pass filter since the Fourier transform of impulse is 1 so it passes all frequency from -∞ to +∞.
10. What do you mean by zero phases of signal?
Ans. If the spectrum of a signal is having even symmetry around zero frequency then the signal is said to have zero phases.
11. What do you mean by linear phase filter?
Ans. Linear phase is a property of a filter, where the phase response of the filter is a linear function of frequency. The result is that all frequency components of the input signal are shifted in time (usually delayed) by the same constant amount (the slope of the linear function), which is referred to as the group delay. And consequently, there is no phase distortion due to the time delay of frequencies relative to one another.
12. What happens if the sampling frequency goes on increasing?
Ans. There is no effect of increasing sampling frequency. It doesn’t increase information in the reconstructed signal as long as sampling frequency is more than Nyquist rate Complexity of the circuit will increase.
13. Example of time-domain aliasing is _______.
Ans. Circular convolution is a suitable example where time-domain aliasing occurs.
14. How FFT speed up the calculation of DFT? (FFT- fast Fourier transform, DFT- discrete Fourier transform)
Ans. In DFT total multiplication required are N2 and addition are N(N – 1) whereas with FFT total multiplication required are log2 N and additions are Nlog2 N. So with FFT calculations required to compute DFT becomes considerably small. FFT is not a transform, its an algorithm.
15. Does zero padding improve the accuracy of the DFT results?
Ans. No zero padding only reduces the spectral spacing and It has nothing to do with the accuracy of DFT.
16. What do you understand by deconvolution?
Ans. Deconvolution is the process of filtering a signal to compensate for an undesired convolution. The concept of deconvolution is widely used in the techniques of signal processing and image processing. Because these techniques are in turn widely used in many scientific and engineering disciplines, deconvolution finds many applications.
17. If the spectrum of a discrete signal is to be expanded then what we have to do?
Ans. We have to decimate the discrete signal so the signal gets spread in the frequency domain.
18. Give relation between resolution and bandwidth.
Ans.
As the bandwidth i.e. main lobe width increase, resolution becomes poor.
19. Which type of sampling is preferred? Baseband sampling or Band-pass sampling.
Ans. Band-pass sampling because in this type of sampling, fs (sampling frequency) required is very small as compared to fs required in baseband sampling.
20. Why LTI systems are so important for analysis?
Ans. LTI systems are important because:
- Because many systems encountered in nature can be successfully modelled as LTI systems.
- LTI systems can be analysed in considerable detail, providing insight into their properties.
21. What is the importance of the unit impulse function?
Ans. One of the important characteristics of unit impulse is that every general signal can be represented as a linear combination of delayed impulses.
22. What are the uses of convolution?
Ans. Convolution is used for:
(i) Provides a useful way to calculate the response of an LTI system.
(ii) It also provides an extremely useful representation for LTI system that allows us to examine their properties in detail.
23. What are mutually orthogonal functions?
Ans. Two vectors are said to be orthogonal if their dot product is zero. i.e. the two vectors have nothing in common.
24. What is a Linear System?
Ans. A linear system is that which obeys the principle of superposition and principle of homogeneity,
for example:
X1 (t) + x2 (t) ↔ Y1 (t) + Y2 (t)
And ax1 (t) + bx2 (t) ↔ ay1 (t) + bY2 (t)
where X(t) is the input to the system and Y(t) is its response
25. Suppose a pulse signal of width T as shown below is transmitted from a RADAR. If after reflection from the target the signal is to be received, then what should be the bandwidth of receiver?
Ans.
The Fourier transform of a pulse signal is shown below.
The 3 – dB bandwidth of the signal is 
.
26. What is the difference between analog and digital signal?
Ans. An analog signal is one in which either signal value is continuous or time is continuous or both are continuous whereas the digital signal is sampled quantized and encoded version of an analog signal.
Analog signal is a continuous wave that keeps on changing over a time period. Digital signal is discrete in nature.
27. Consider the block diagram shown below:
Input → Sampling → Quantization → output
If input is an analog signal then output is _______
Ans. According to the definition of an analog and digital signal, it is a digital signal.
28. How DTFT is related to CTFT? (DTFT- discrete-time Fourier transform , CTFT- continuous-time Fourier transform)
Ans. An energy signal obeying Dirichlet condition can have CTFT and its spectrum is aperiodic and continuous. If the same signal is sampled and them its Fourier transform is obtained then it is DTFT and the spectrum is continuous and periodic.
29. If a signal is discrete and periodic in the time domain then in the frequency domain the nature of the signal is?
Ans. Since periodicity in one domain reveals discrete in other domain so if the signal is discrete and periodic in one domain then it is periodic and discrete in other domain.
30. What is the difference between convolution and correlation?
Ans. Correlation is a measurement of the similarity between two signals/sequences.
Convolution is the measurement of the effect of one signal on the other signal.
The mathematical calculation of Correlation is same as a convolution in the time domain, except that the signal is not reversed, before the multiplication process. If the filter is symmetric then the output of both the expression would be the same.
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