Fourier transform. Spectral analysis brief theoretical review fourier analysis

Variants	1	2	3	4	5	6	7	8
9
Signal’s shape	cosine	sine	cosine	sine	cosine	sine	cosine	sine	cosine
f (Hz)	10	25	40	20	10	30	20	30	40
a	1	3	0.5	2	0.5	4	1	3	2.5

Define Magnitude (Power), Amplitude and Phase for the FFT of the signal. Attach the plot.

3. 
   Create in Simulink environment a model given in Figure 3 and perform simulation. The model includes a generator for sine curve, buffer, window function, FFT, vector scope and block for magnitude and phase estimation. These blocks could be easily found within Signal Processing Blockset of Simulink Library. Thus, take the generator for sine curve from Signal Processing Sources. Buffer block take from Signal Management Library. Window Function block is situated in Signal Operations Library. FFT block is situated in Transforms Library; from Math Operations Library take Complex to Magnitude-Angle Block and Vector Scope could be found in Signal Processing Sinks Library.
   

Figure 3. Simulation model
On the next stage in is necessary to adjust above given blocks. Their properties are necessary to be set as follows:
Sine Wave Source Block:

• 
  Sample Model set to Discrete;
  
• 
  Output complexity set to Real;
  

Complex to Magnitude-Angle Block: define output to Magnitude;
Vector Scope block: find Axis properties toolbar and set frequency rage to [-Fs/2…Fs/2] and Frequency Unit: Hertz;
Simulate a sine curve with amplitude 1 and frequency of 1KHz. Sampling time set to 8KHz. The output signal select to be a real. Set the size buffer to 16. Choose Window Function to be Blackman. Obtain the spectrum for different types of frequency range. Explain the obtained results.


Report
1 Submit your Matlab code.
2 Submit your calculation and hand sketch of the signal.
3 Submit the plot of magnitude (power), Amplitude and Phase of the signal.