If the analog signal to be quantized is a sinusoidal waveform, that is, x(t)= 9:5 sin (2000× _t), and if the bipolar quantizer uses 6 bits, determine a. number of quantization levels; b. quantization step size or resolution, D, assuming that the signal range is from 10 to 10 volts; c. the signal power to quantization noise power ratio.

Design a fourth-order digital lowpass Butterworth filter with a cutoff frequency of 2 kHz and a passband ripple of 3 dB 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. A system is described by the difference equation y(n)  -0.5y(n-1) + 0.06y(n-2) = (0.4)^n-1 u(n-1): Determine the solution when the initial conditions are y(-1) = 1 and y(-2) = 2. 2. Given the following difference equation with the input-output relationship of a certain initially relaxed system (all initial conditions are zero), y(n)-0.7y(n-1) + 0.1y(n-2) = x(n) + x(n-1), a. find the impulse response sequence […]

1. Find the z-transform for each of the following sequences: a. x(n)=4u(n)n b. x(n)=(-0.7)^n u(n) c. x(n)=4e^-2n u(n) d. x(n)=4(0.8)^n cos (0.1_n)u(n) e. x(n)=4e^-3n sin (0.1 _n)u(n). 2. Using the properties of the z-transform, find the z-transform for each of the following sequences: a. x(n)=u(n)+(0.5)^n u(n) b. x(n)=e^-3(n-4) cos [0.1 _(n-4)]u(n-4), where u(n-4)=1 for n _ 4 while u(n-4) ¼ 0 for n

Using the sum of sinusoids in Problem. a. Generate the sum of sinusoids for 240 samples using a sampling rate of 8000 Hz. b. Write a MATLAB program to compute and plot the amplitute spectrum of the signal x(n) with the FFT and using each of the following window functions (1) Rectangular window (no window) (2) Triangular window (3) Hamming window c. Examine the effect […]

1. Determine which of the following linear systems is causal. a. y(n) = 0.5x(n) + 100x(n-2)  20x(n-10) b. y(n) = x(n + 4) + 0.5x(n)  2x(n-2) 2. Determine the causality for each of the following linear systems. a. y(n) = 0:5x(n) þ 20x(n  2)  0:1y(n  1) b. y(n) = x(n+2)  0.4y(n-1) c. y(n) = x(n-1) + 0.5y(n+2)

Design a 41-tap bandpass FIR filter with the lower and upper cutoff frequencies being 2,500 Hz and 3,000 Hz, respectively, using the following window functions. Assume a sampling frequency of 8,000Hz. a. Hanning window function b. Blackman window function. List the FIR filter coefficients and plot the frequency responses for each design.

Given a DSP system for noise cancellation application with a sampling rate set up to be 8,000 Hz, as shown, the desired signal of a 1,000 Hz tone is generated internally via a tone generator; and the generated tone is corrupted by the noise captured from a microphone. An adaptive FIR filter with 25 taps is applied to reduce the noise in the corrupted tone. […]

Given the audio system with the following specifications: Audio input frequency range: 0  15 kHz ADC resolution ¼ 16 bits Current sampling rate ¼ 30 kHz, a. determine the oversampling rate if the 12-bit ADC chip is used to replace the audio system; b. draw the block diagram.

In Previous Problem, if we use an IIR filter with the following specifications: Sampling rate: 8,000 Hz Butterworth IIR filter Frequency range to be emphasized: 1,500–2,000 Hz Lower stop band: 0–1,000 Hz Upper stop band: 2,500–4,000 Hz Passband ripple: 3 dB Stopband attenuation: 20 dB, determine the filter order and filter transfer function. Use MATLAB