Prepare the answers of the following questions.

Questions for Problem 1

1.1 Which of the following is experienced during down-sampling?
 (a) Bandwidth contraction
 (b) Bandwidth expansion 
 (c) Both of the above depending on the input frequency band
 (d) Bandwidth remains the same

1.2 For a signal that is Bandlimited  to B and is sufficiently over sampled at 6B, which of the following is true. 
 (a) We may avoid using an antialiasing filter before down-sampling by 2
 (b) We have to use a filter to avoid aliasing
 (c) Antialiasing filter is needed regardless of the above. 

1.3 We use a reconstruction filter after up-sampling for the following reason. 
 (a) To get rid of the imaging component in the spectra. 
 (b) To interpolate the signal in the time domain.
 (c) Both of the above.
 (d) None of the above.

1.4 Give two applications of down sampling and up sampling.   

Questions for Problem 2
2.1 The cut-off frequency of the overall filter is 
 (a) 2pi/3
 (b) pi/3
 (c) 2pi
 (d) 3pi/2

Questions for Problem 3
3.1 Which of the following is true for the QMF filters used in this problem?
 (a) F1(z) = G2(z) and F2(z) = -G1(-z) 
 (b) G2(-z)F2(z) = -G1(-z)F1(z)
 (c) F1(z) = G2(-z) and F2(z) = -G1(-z) 
 (d) F1(z) = G2(z) and F2(z) = G1(-z)  

3.2 Which of the following is true for the QMF filters used in this problem?
 (a) The output reconstructed signal should have same amplitude as input but overall delayed by one sample.  
 (b) The output reconstructed signal should have double the amplitude as input but overall delayed by two samples.  
 (c) The output reconstructed signal should have triple the amplitude as input but overall delayed by one sample.  
 (d) The output reconstructed signal should have half the amplitude as input but overall delayed by one sample.  

3.3 Where should we place the quantizer (encoder) and inverse quantizer (decoder) when QMF filters are used in subband coding of speech?
 (a) before the down sampler in analysis filter bank and after the up sampler in synthesis filter bank.
 (b) after the down sampler in analysis filter bank and before the up sampler in synthesis filter bank.
 (c) before the down sampler in analysis filter bank and before the up sampler in synthesis filter bank.
 (d) after the down sampler in analysis filter bank and after the up sampler in synthesis filter bank.

3.4 The purpose of using a quantizer and an inverse quantizer in each sub-band of QMF filters is (consider speech signal)
 (a) To allocate fewer bits per sample in higher sub-bands and thereby achieve compression. 
 (b) To allocate more bits per sample in higher sub-bands and thereby achieve compression. 
 (c) To ensure zero delay in the filter bank.   
 (d) To allocate more bits per sample in the middle sub-bands and thereby achieve compression. 

3.5 Which filters (among G1, G2, F1, F2) are  low pass and which filters are high pass? 

3.6  Was the reconstructed signal  worse (see problem 3, questions (3) and (4))? If yes, why? If not, why?

Questions for Problem 4
4.1 If the input has at 4 kHz Bandwidth, the frequency Bandwidth at point d is (consider ideal low pass and high pass filtering) 
 (a) 0-4 kHz
 (b) 1-2 kHz
 (c) 2-4 kHz
 (d) 0-1 kHz

4.2 Describe a QMF filter Bank based on what you learned  from problem 4, that gives sub-band resolutions of pi/8.

Place 17 figures in one word file and label them.