6. Next you will examine a windowed signal in the frequency domain. Set up a cosine wave as in Part 4 of this lab and wi

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6 Next You Will Examine A Windowed Signal In The Frequency Domain Set Up A Cosine Wave As In Part 4 Of This Lab And Wi 1 (52.08 KiB) Viewed 14 times

6. Next you will examine a windowed signal in the frequency domain. Set up a cosine wave as in Part 4 of this lab and window the signal x as shown below: win = hamming (M); xwin = x.*win'; Look at xwin in the time and frequency domains in exactly the way you did for x (in Part 4 a & b). Repeat this using the Blackman window. Compare between part 4 and 6 in terms of spectral leakage. Frequency resolution is the smallest difference in frequency that can be distinguished. It is defined by: Af = 1/sampling duration=1/(Ts* number of sampling points) Suppose we are having two sine waves xl & x2 of frequencies fl= 1000 Hz, f2= 1003 Hz respectively. These two are added to create a new signal x (i.e. x=x1+x2). Fs=48000 Hz, Ts=1/48000 sec, Sampling point: 8192 & FFT size: 8192 The Frequency resolution is: 48000/8192-5.86 Hz> 3 Hz It can be seen that in the frequency domain, the two components cannot be distinguished. The real frequency resolution can be increased by increasing the sampling duration. There are two ways to increase the sampling duration (Increase the number of sampling points or Decrease the sampling frequency). If the sampling points are increased to 32768, the frequency resolution becomes: 48000/32768=1.46 Hz> 3 Hz which is enough to resolve the two said frequencies.