(Aktu Btech) Digital Signal Processing Important Unit-5 Multirate Digital Signal Processing (MDSP)

The B.Tech. AKTU Quantum Book will help you master the skill of digital signal processing. Gain access to crucial notes, frequent queries, and insightful knowledge in this area. Unit-5 Multirate Digital Signal Processing (MDSP)

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Important Questions For Digital Signal Processing:
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Q1. What is multirate digital signal processing ? Discuss about application areas of it.

Ans. A. Multirate digital signal processing: 

• 1. Sampling rate conversion refers to the process of transforming a signal from one rate to another. Multirate digital signal processing systems are those that use several sample rates to process digital signals.
• 2. With an upsampler and a downsampler, different sampling rates can be achieved. To accomplish this, the basic procedures of multirate processing are decimation and interpolation.
• 3. Decimation is used to reduce the sample rate, whereas interpolation is used to increase the sampling rate.

B. Applications:

• i. Sub-band coding (speech, image) 
• ii. Voice privacy using analog phone lines 
• iii. Signal compression by subsampling 
• iv. A/D, D/A converters. 

C. Application area of multirate signal processing: 

There are various areas in which multirate signal processing is used:

• i. Communication systems 
• ii. Speech and audio processing systems 
• iii. Antenna systems, and 
• iv. Radar systems 

Q2. Explain subband coding of speech signals. 

Ans. 1. Subband coding is a method, where the speech signal is subdivided into several frequency bands and each band is digitally encoded separately. 

• 2. Filter design is crucial in getting good subband performance coding. Aliasing caused by decimation of subband signals must be minimized.
• 3. Using Quadrature Mirror Filters (QMF) with the frequency response characteristics indicated in Fig. 4 is a feasible solution to the aliasing problem. The subband encoded speech signal generation approach is essentially the inverse of the encoding procedure.
• 5. As illustrated in Fig. 5, signals in nearby low-pass and high-pass frequency regions are interpolated, filtered, and merged. For each octave of the signal, a pair of (QMF) is employed in signal synthesis.
• 6 Subband coding is also an effective method to achieve data compression in image signal processing by combining subband coding with vector quantization for each subband signal.

• 7. When the signal energy is concentrated in a certain section of the frequency band, subband coding of signals is an effective way for accomplishing bandwidth compression in a digital representation of the signal.

Q3. Obtain the two-fold expanded signal y(n) of the input signal x(n) 

Ans. 1. The output signal y(n) is given by 

2. In general, to obtain the expanded signal y(n) by a factor I, (I- 1) zeros are inserted between the samples of the original signal x(n).

3. The z-transform of the expanded signal is 

4. The input and output signals are shown in Fig. 

Q4. Discuss modulation free method for decimation and interpolation.

Ans. A. Modulation free method for decimation: 

1. Decimation of the sampled bandpass signal whose spectrum is shown in Fig. Note that the signal spectrum is confined to the frequency range,

2. A bandpass filter would normally be used to eliminate signal components outside the frequency desired of the frequency range. Then direct decimation bandpass signal by the factor D results in the Fig. spectrum shown in 5.8.2(a), for m odd, and Fig. 5.8.2(b) for m even.

3. In the case where m is odd, there is an inversion of the spectrum of the signal. This inversion can be undone by multiplying each sample of the decimation signal by (-1)_n, n = 0, 1, …

B. Modulation free method for interpolation: 

• 1 Modulation free interpolation of a bandpass signal by an integer factor I can be accomplished in a similar manner. The process of upsampling by inserting zeros between samples of x(n) produces I image in the band 0 ≤ ω ≤ 𝝅. The desired image can be selected by bandpass filtering.
• 2. Note that the process of interpolation also provides us with the opportunity to achieve frequency translation of the spectrum. 

Q5. A one stage decimator is characterized by the following :

Decimation factor = 3

Anti-aliasing filter coefficients

Given the data, r(n) with successive values [6, – 2, – 3, 8, 6, 4,- 2], calculate and list the filtered output w(n) and the output of the decimator y(m). 

Ans.

Filtered output:

Decimator output :

Q6. Suppose that the input signal has a flat spectrum between – 0.8𝝅 and 0.8𝝅. Determine the number of subfilters to achieve a signal to distortion ratio of 50 dB when linear interpolation is applied. 

Ans. 

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