# Digital Signal Processing Questions and Answers – Digital to Analog Conversion Sample and Hold

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This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “Digital to Analog Conversion Sample and Hold”.

1. What is the ideal reconstruction formula or ideal interpolation formula for x(t) = _________
a) $$\sum_{-\infty}^\infty x(nT) \frac{sin⁡(π/T) (t-nT)}{(π/T)(t-nT)}$$
b) $$\sum_{-\infty}^\infty x(nT) \frac{sin⁡(π/T) (t+nT)}{π/T)(t+nT}$$
c) $$\sum_{-\infty}^\infty x(nT) \frac{sin⁡(2π/T) (t-nT)}{2π/T)(t-nT}$$
d) $$\sum_{-\infty}^\infty x(nT) \frac{sin⁡(4π/T) (t-nT)}{(4π/T)(t-nT)}$$

Explanation: x(t) = $$\sum_{-\infty}^\infty x(nT) \frac{sin⁡(π/T) (t-nT)}{(π/T)(t-nT)}$$ where the sampling interval T = 1/Fs=1/2B, Fs is the sampling frequency and B is the bandwidth of the analog signal.

2. What is the new ideal interpolation formula described after few problems with previous one?
a) g(t)=$$\frac{sin⁡(2πt/T)}{(πt/T)}$$
b) g(t)=$$\frac{sin⁡(πt/T)}{(πt/T)}$$
c) g(t)=$$\frac{sin⁡(6 πt/T)}{(πt/T)}$$
d) g(t)=$$\frac{sin⁡(3 πt/T)}{(πt/T)}$$

Explanation: The reconstruction of the signal x (t) from its samples as an interpolation problem and have described the function:g(t)=$$\frac{sin⁡(πt/T)}{(πt/T)}$$.

3. What is the frequency response of the analog filter corresponding to the ideal interpolator?
a) H(F)=$$\begin{cases}T, |F|≤ \frac{1}{2T} = F_s/2\\0,|F| > \frac{1}{4T}\end{cases}$$
b) H(F)=$$\begin{cases}T, |F|≥ \frac{1}{2T} = F_s/2\\0,|F| > \frac{1}{4T}\end{cases}$$
c) H(F)=$$\begin{cases}T, |F|≤ \frac{1}{2T} = F_s/2\\0,|F| > \frac{1}{2T}\end{cases}$$
d) H(F)=$$\begin{cases}T, |F|≤ \frac{1}{4T} = F_s/2\\0,|F| > \frac{1}{4T}\end{cases}$$

Explanation: The analog filter corresponding to the ideal interpolator has a frequency response:
H(F)=$$\begin{cases}T, |F|≤ \frac{1}{2T} = F_s/2\\0,|F| > \frac{1}{2T}\end{cases}$$, H(F) is the Fourier transform of the interpolation function g(t).
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4. The reconstruction of the signal from its samples as a linear filtering process in which a discrete-time sequence of short pulses (ideally impulses) with amplitudes equal to the signal samples, excites an analog filter.
a) True
b) False

Explanation: The reconstruction of the signal from its samples as a linear filtering process in which a discrete-time sequence of short pulses (ideally impulses) with amplitudes equal to the signal samples, excites an analog filter.

5. The ideal reconstruction filter is an ideal low pass filter and its impulse response extends for all time.
a) True
b) False

Explanation: The ideal reconstruction filter is an ideal low pass filter and its impulse response extends for all time. Hence the filter is noncausal and physically nonrealizable. Although the interpolation filter with impulse response given can be approximated closely with some delay, the resulting function is still impractical for most applications where D/A conversion are required.

6. D/A conversion is usually performed by combining a D/A converter with a sample-and-hold (S/H ) and followed by a low pass (smoothing) filter.
a) True
b) False

Explanation: D/A conversion is usually performed by combining a D/A converter with a sample-and hold (S/H) and followed by a low pass (smoothing) filter. The D/A converter accepts at its input, electrical signals that correspond to a binary word, and produces an output voltage or current that is proportional to the value of the binary word.

7. The time required for the output of the D/A converter to reach and remain within a given fraction of the final value, after application of the input code word is called?
a) Converting time
b) Setting time
c) Both Converting & Setting time
d) None of the mentioned

Explanation: An important parameter of a D/A converter is its settling time, which is defined as the time required for the output of the D/A converter to reach and remain within a given fraction (usually,±1/2 LSB) of the final value, after application of the input code word.

8. In D/A converter, the application of the input code word results in a high-amplitude transient, called?
a) Glitch
b) Deglitch
c) Glitter
d) None of the mentioned

Explanation: The application of the input code word results in a high-amplitude transient, called a “glitch”. This is especially the case when two consecutive code words to the A/D differ by several bits.

9. In a D/A converter, the usual way to solve the glitch is to use deglitcher. How is the Deglitcher designed?
a) By using a low pass filter
b) By using a S/H circuit
c) By using a low pass filter & S/H circuit
d) None of the mentioned

Explanation: The usual way to remedy this problem is to use an S/H circuit designed to serve as a “deglitcher”. Hence the basic task of the S/H is to hold the output of the D/A converter constant at the previous output value until the new sample at the output of the D/A reaches steady state, and then it samples and holds the new value in the next sampling interval. Thus the S/H approximates the analog signal by a series of rectangular pulses whose height is equal to the corresponding value of the signal pulse.

10. What is the impulse response of an S/H, when viewed as a linear filter?
a) h(t)=$$\begin{cases}1,0≤t≤T\\0,otherwise\end{cases}$$
b) h(t)=$$\begin{cases}1,0≥t≥T\\0,otherwise\end{cases}$$
c) h(t)=$$\begin{cases}1,0<t≤T\\0,otherwise\end{cases}$$
d) None of the mentioned

Explanation: W hen viewed as a linear filter, the S/H has an impulse response:
h(t)=$$\begin{cases}1,0≤t≤T\\0,otherwise\end{cases}$$

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