Digital Signal Processing and Application

Define energy signal and power signal. Is the signal $x[n]=\cos (\frac{\pi }{5}n)\sin (\frac{\pi }{3}n)$ periodic? If it is periodic, determine the fundamental period.

Find the output of an LTI system having impulse response $h[n]=\{1,3,2,-1,1\}$ to the input $x[n]=2\delta [n]-\delta [n-1]$.

Compute the lattice-ladder coefficients for the given IIR system: $$H(z)=\frac{1+2z^{-1}+2z^{-2}+z^{-3}}{1+\frac{13}{24}{z}^{-1}+\frac{5}{8}{z}^{-2}+\frac{1}{3}{z}^{-3}}$$ Also, comment on the stability and draw the lattice-ladder structure for the system.

Define Gibb's phenomenon. The desired frequency response of a HPF is given by

Design a linear phase FIR filter using hamming window for $M=7$ and ${\omega }_c=2$ rad/sample.

What do you understand by optimum filter? Describe Remez exchange algorithm for FIR filter design using a flowchart.

Compare and contrast between impulse invariance method and bilinear transformation method. Design a digital IIR low pass filter using bilinear transformation based on Butterworth approximation to meet the following specifications: passband magnitude characteristics that is constant to within 1 dB for recurrences below $\omega =0.2\pi$ and stopband attenuation of at least 15 dB for frequencies between $\omega =0.3\pi$ and $\pi$. Use bilinear transformation.

Find 8-point DFT using DIF-FFT of the sequence $x[n]=\{1,2,3,2,1\}$.

Discuss the application of DSP in Power System Monitoring and Diagnostics. Perform the circular convolution of the following two sequences $x_1[n]=\{1,2,3\}$ and $x_2[n]=\{1,2,3,4\}$