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CAN310 Coursework 1

Notice:
1. Deadline: May 16th, 23:59.
2. Submission: upload on LMO

A Matlab live script file (.mlx), including your report and the Matlab codes. Please make sure your Matlab code can run smoothly without any bug or error, since assessors won't debug your code.

3. The report is NOT a formal report, so there is no need to write introduction, background, etc. Just be concise and accurate. For each question, there should be two or three parts: code, result, discussion or comparison (if necessary).
4. This lab will take 15% in the final mark.
5. Code or report similarity will be regarded as plagiarism. Generative Al is NOT allowed to use.

Description:

An FIR filter is described in Table 1. Properties of some fixed window functions is given in Table 2.
Table 1. FIR filter parameter

passband ripple, Ap	1dB
stopband attenuation, As	15 dB
passband edge frequency, Wp	0.2π
stopband edge frequency, ws	0.35π

Table 2. Properties of some fixed window functions

Window Type	Main Lobe width OmL	Transition bandwidth	Relative Sidelobe Level As (dB)	Minimum Stopband Attenuation as (dB)
Rectangular	4π/(2M+1)	0.92π/M	13.3	20.9
Hanning	8π/(2M+1)	3.11π/M	31.5	43.9
Hamming	8π/(2M+1)	3.32π/M	42.7	54.5
Blackman	12π/(2M+1)	5.56π/M	58.1	75.3

Questions:
1. Design an FIR filter satisfying the parameters in Table 1. Choose one window type in Table 2. Calculate the needed length, transition bandwidth, and cutoff frequency of the filter.
2. Plot the impulse response of the filter.
3. Plot the amplitude and phase response of the filter.
4. Compare FIR filter's amplitude and phase responses with those of IIR filter.
5. Generate 4 sinusoidal waves, with frequencies 0.15 π, 0.3 π, 0.4 π, 0.86 π. Let them pass the filter described in Table 1. And plot the waveforms before and after the filter.
6. Plot the amplitude responses of the 4 windows in Table 2. Compare the responses. Use dot lines to highlight 3 dB bandwidth and 20 dB bandwidth.

Marking criteria:

Report writing and formatting.	30%
Programming style, including the function usage, comments, etc.	30%
Results accuracy and discussions.	40%