ELEC8040: Project - The Design of 16-Point Complex FFT Processor - MATLAB Assignment Help

Assignment Task:

Task:

The project is concerned with the design of 16-point complex FFT processor using radix-2, Decimation-in-Time (DIT) butterfly architecture. The following MATLAB function is provided to you to use in the project: res_analysis.

The project consists of two parts:

Part A

(i) Design and implement a 16-point radix-2 DIT complex FFT in MATLAB using complex variables, exp(–j*x) for twiddle factor WN calculations (e.g. no storage for the twiddle factors is required), and one or more 16-element arrays for the data memory. Assume that all the input time domain data values are available in a 16-element array to start with. Inputs and outputs are all complex values.

(ii) Show that your FFT correctly calculates an FFT for a random input, Din, by comparing it in MATLAB using input signal:

>>Din = (1.99*rand(1,16)-1) + j*(1.99*rand(1,16)-1);
and:
>>res_analysis(fft(Din)*Scale, YourFFTOutput);
where Scale is a real valued constant specific to your design and YourFFTOutput is the output of your FFT implementation. Submit as part of your typed report:

(1) 16-Point, radix-2, DIT FFT Signal Flow Graph (SFG) showing butterflies for each stage and their associated data input/output locations and twiddle factors.

(2) Block diagram representing your scaled butterfly and high-level diagram showing the overall FFT processor implementation in MATLAB.

(3) res_analysis() plot and res_analysis() text output

(4) Discussion about how you have tested the MATLAB code to verify correct operation.

(5) Your fully commented MATLAB code.
 

Part B

(i) Repeat the requirements in Part A but now the input, output, and all values between stages must be 16-bit values with valid ranges matching 16-bit 2's complement numbers. Use “Convergent” to round extra bits from wide numbers at the end of each butterfly computation. The twiddle factors WN are also quantised to 16-bit 2’s complement numbers.

(ii) State the Q[n.m] number format for the input, output, and all values between stages as well as the twiddle factors. Where, n represents the number of integers bits and m the number of fractional bits.

(iii) Repeat Part A (ii) and demonstrate the effect of data and coefficient quantisation on the output of your implemented FFT processor. Submit as part of your typed report:

(5) Block diagram representing your quantised butterfly and overall FFT implementation showing where the quantization and scaling taking place.

(6) res_analysis() plot and res_analysis() text output

(7) Discussion about how you have tested the MATLAB code to verify correct operation.

(8) Your fully commented MATLAB code.

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