Asgn1
Assignment no. 1  
Subject : DSP TE : Sem I  
1.  State and Explain Sampling Theorem. 
2.  Consider the analog signal Xa(t)=3cos2000πt +5sin6000πt+10cos12,000t. 1. What is the Nyquist rate for this signal? 2. If this analog signal is sampled st Fs=5000 samples/sec, what is the discretetime obtained after sampling.? 3. What is the analog signal ya(t) we can reconstruct from the samples if we use ideal interpolation? 
3.  Explain basic block diagram of Digital Signal Processing with its functions. 
4.  Explain concept of Orthogonolity. Show that the basis matrix for DFT is Orthogonal. Consider N=4. 
5.  Determine the fundamental period of the following sinusoidal signals.

6.  Consider the analog signal Xa(t)=3cos200πt 1. What is minimum sampling rate to avoid aliasing? 2. If this analog signal is sampled at Fs=400 Hz , what is the discretetime obtained after sampling.? 3. If this analog signal is sampled at Fs=150 Hz , what is the discretetime obtained after sampling.? 4. What is the frequency F in between 0<F<Fs/2 of sinusoidal that yields samples identical to those in part? 
7.  List advantages and disadvantages of DSP over analog signal processing. 