### Question:

What to submit: Your coursework must be submitted as a report in Word format to Turnitin. All MATLAB scripts used must be included as appendices at the end of the report and numbered according to the corresponding questions. All code lines must be commented to explain them. All sources used in the report must be cited. All references must be in IEEE format. Please note that 5 marks will be allocated to the presentation and organisation of your report.

**Part I**

1)Use MATLAB to design a bounded-input bounded-output (BIBO) stable lowpass infinite impulse response (IIR) digital filter, which, if used after sampling an analogue signal with sampling rate 10 kHz, can attenuate signals with frequencies higher than 200 Hz. Plot the magnitude response and the phase response of the filter. Discuss your results.

2)Apply your filter to the MATLAB built-in audio signal ‘chirp’. Listen to the original signal and to the filtered signal and comment.

3)Use the MATLAB function spectrogram to plot the spectrogram of the original ‘chirp’ signal and the spectrogram of the signal after applying your filter. Your plots must show time on the x-axis. Discuss the plots.

a)Show that the signal x[n]=16sin5 n-20sin3 n+5sin n can be written in the form Asin(ωn+φ), where A, ω, and φ are real numbers.

b)Hence, find a simple mathematical expression for the output signal if your filter is applied to the signal x[n].

**Part II**

The signal stored in the file problem2.mat was obtained by sampling a signal x(t) with a sampling rate of 500 Hz. Use the discrete Fourier transform (DFT) to analyse the frequency content of the signal x(t).

**Part III**

1)Write a MATLAB function that takes as input arguments a 512×512 grayscale image and an integer n (0

(1) partitions the image into 8×8 blocks,

(2) computes the 2D-discrete cosine transform (DCT) of each block,

(3) orders the DCT coefficients in each block according to the zig-zag scan,

(4) sets the last n coefficients in each block to zero,

(5) computes the inverse 2D-DCT of each block of coefficients, and

(6) displays the resulting image.

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