Design a fourth-order digital lowpass Chebyshev filter with a cutoff frequency of 1.5 kHz and a 0.5 dB ripple at a sampling frequency of 8,000 Hz. a. Determine the transfer function and difference equation. b. Use MATLAB to plot the magnitude and phase frequency responses.

1. Determine which of the following is a linear system. a. y(n) = 5x(n) + 2x²(n) b. y(n) = x (n-1) + 4x(n) c. y(n) = 4×3(n-1)  2x(n) 2. Given the following linear systems, find which one is time invariant. a. y(n) = 5x(n-10) b. y(n) = 4x(n²)

Given a speech equalizer shown in Figure to compensate midrange frequency loss of hearing: Sampling rate = 8,000 Hz Bandpass FIR filter with Hamming window Frequency range to be emphasized = 1,500–2,000 Hz Lower stopband = 0–1,000 Hz Upper stopband = 2,500–4,000 Hz Passband ripple = 0.1 dB Stopband attenuation = 45 dB, determine the filter length and the lower and upper cutoff frequencies.

Given an FIR lowpass filter design with the following specifications: Passband = 0–800 Hz Stopband = 1,200–4,000 Hz Passband ripple = 0.1 dB Stopband attenuation = 40 dB Sampling rate = 8,000 Hz, determine the following: a. window method b. length of the FIR filter c. cutoff frequency for the design equation.

For a single-stage decimator with the following specifications: Original sampling rate ¼ 8 kHz Decimation factor M ¼ 4 Frequency of interest ¼ 0800 Hz Passband ripple ¼ 0:02 dB Stopband attenuation ¼ 46 dB, a. draw the block diagram for the decimator; b. determine the window type, filter length, and cutoff frequency if the window method is used for the anti-aliasing FIR filter design.

Given a DSP system in which a sampling rate of 8,000 Hz is used and the anti-aliasing filter is a Butterworth lowpass filter with a cutoff frequency of 3.2 kHz, determine the order of the Butterworth lowpass filter for the percentage of aliasing level at the cutoff frequency required to be less than 10%.

Given a filter a. plot the magnitude frequency response and phase response using MATLAB; b. specify the type of filtering; c. find the difference equation; d. perform filtering, that is, calculate y(n) for the first 1,000 samples for each of the following inputs and plot the filter outputs using MATLAB, assuming that all initial conditions are zeros and the sampling rate is 8,000 Hz: e. […]

Design a bandpass FIR filter with the following specifications: Design method: Parks-McClellan algorithm Sampling rate: 8000 Hz Passband: 1200 – 1600 Hz Lower stopband 0 – 800 Hz Upper stopband 2000 – 4000 Hz Passband ripple: 1 dB Stopband attenuation: 40 dB List the filter coefficients and plot the frequency responses.

1. Given the following data sequence with a length of 6, x(0)=0, x(1)=1, x(2)=0, x(3)=1, x(4)=0, x(5)=1 compute the windowed sequence Xw(n) using the a. Triangular window function. b. Hamming window function. c. Hanning window function. 2. Given the sequence in Figure. where fs=100 Hz and T=0.01 sec, compute the amplitude spectrum, phase spectrum, and power spectrum using the a. Triangular window. b. Hamming window. […]