Q1 A sine wave is sampled at interval and quantixed using bits precision over th

Q1
A sine wave is sampled at interval and quantixed using bits precision over the range . The sine wave has peroid and is chosed such that . Plot one cycle of the true signal and show where the sample od the sinusoidal waveform fall.
Q1
A sine wave is sampled at interval and quantixed using bits precision over the range . The sine wave has peroid and is chosed such that . Plot one cycle of the true signal and show where the sample od the sinusoidal waveform fall.
Show Time Quantization and Amplitude Quantization
Q2
i)For a 3 term averagin filter write a difference eqatuon governing the filter and dervie the corresponding z transform
Sketch a pole zero plot would this filter be stable why or why not?
ii) Sketch the frequency resoponce and explain where the peaks and nulls occur
iii)Exten d the above to an N-term averging filter write a difference equation and derive the ztransform in closed form
Indicatate were the pole and zeros would fall for Larger N and then sketch the frequency response for a similarlary large N
Q3
i)A sionusodial signal has the form
Derive an expression for the autocorrelation
II) Explain the significance of this result in term of the frequency of the correlation and also if noise were added to the sinusoidal signal
iii) If a signal is corrupt by additive white noise then the resulting signal would be
What form would the autocorrelation take in that case?
Q4
A band pass FIR filter is required to pass frequencies from 5KHz to 8KHz using a sample rate of 40K
i) Explain how this would map to normalization sampling frequencies in radians per sample Include a diagram shown the passband stop band and other areas of interest
ii) Derive a mathematical expression for the filter coefficients
iii) Write a MATLAB script to calculate the frequency response of the filter and briefly explain how it works.
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