Digital Signal Processing

ENGT5111 Digital Signal Processing

2019-20

 

Filter Design and Image Processing

(Resit Assignment)

(Maximum Marks: 50)

 

 

Issue date: 04/07/2020

Submission deadline: 04/09/2020

Feedback: 25/09/2020

 

 

 

 

 

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 (Filter design and signal analysis)

 

Problem 1                                                                                                                                         

 

1)      Use MATLAB to design a bounded-input bounded-output (BIBO) stable lowpass IIR filter with sampling frequency 8192 Hz and cut-off frequency 300 Hz. Plot the magnitude response, phase response, and pole-zero plot of the filter. Discuss your results.

                                                                                                                        (10 marks)

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

                                                                                                                          (5 marks)                                                                                                                            

3)      Use the MATLAB function spectrogram to plot the spectrogram of the original ‘handel’ signal and the spectrogram of the filtered signal. Your plots must show time on the x-axis. Discuss the plots.

                                                                                                                        (8 marks)

4)      Repeat part 2) and part 3) for the MATLAB built-in signal ‘chirp’.

                                                                                                                        (2 marks)                                                                                                                                                                                                                                                                                                                

5)      Find a simple mathematical expression for the output signal if your filter is applied to the signal x[n]=16sin⁵(0.02πn)-20sin³(0.02πn)+5sin(0.02πn).   

                                                                                                                          (5 marks)                                                                                               

 

                                                                                  

Part II (Image Processing)

 

                                                                                                                        

Problem 2               

                                                                                                                                                      

1)      Write a MATLAB function that takes as input arguments a 512x512 grayscale image and an integer n (0<n<65), (1) partitions the image into 8x8 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.                                                                           (10 marks)                                                                                  

 

2)      Plot the peak signal-to-noise ratio (PSNR) for n=1, 2, 4, 8, 16, 32, 64 when the input image in part 1) is ‘boat.512’ (Fishing Boat) from  http://sipi.usc.edu/database/database.php?volume=misc. Show the reconstructed image each time. Discuss the results.   

                                                                                                                                      (5 marks)