ASSIGNMENT-1

http://dsp-sumit.blogspot.com/2012/08/blog-post.html

                                                               Assignment-1

Q.1. The first five points of an 8-point DFT of a real valued sequence are given as: {0.25, 0.125-j0.3018, 0, 0.0125-j0.0518, 0} Determine the remaining 3 points?

Q.2. Compute 8-point circular convolution of the following set of sequences:

(i) x₁(n)={1,1,1,1,0,0,0,0}

    X₂(n)=sin(3*pi*n/8) , 0≤n≤7 .

(ii) x₁(n)= (1/4)^n  ,0≤n≤7 .

    X₂(n)= Cos(3*pi*n/8) , 0≤n≤7 .

Q.3. Compute the 6-point DFT of the given sequence(without using matrix method) as:

X(n)= {3,2,1,0,1,2}

Q.4. Compute the 4-point DFT of the given sequence using Linear transformation technique:

X(n)={1,1,2,2}. Also explain the symmetry property of Twiddle factor?

Q.5. Discuss the impacts of spectral leakage and explain its relationship  w.r.t  DFT?

Q.6.Explain briefly the sampling of DTFT to obtain DFT . Also justify the physical importance of the same?

Q.7.Discuss the relationship of DFT with the periodic Fourier series coefficients?

Q.8.Explain the Gibb’s Phenomenon and its significance (Refer: J.G Proakis)?

Q.9.Justify that the Continuous-Time Fourier transform is derived from Continuous-Time Fourier series approximation?

Q.10.Describe Mat lab tool and some of its basis functions used in signal processing?

INSTRUCTOR: Mr. Sumit Joshi