Hi the question I am asking is that I am using Matlab and I need to plot the Fast Fourier Transform of these functions using the Fast Fourier transform "fft(function)" in Matlab not the regular Fourier Transform function. I also need to take the absolute value of the Fast Fourier transform calculation so it gives the magnitude when plotted. All of the functions are in the time range from -5 to 5 seconds. The rectangular pulse is the only function which does not have a time range. The time range is (-5)<=t<=5 seconds for all functions except the rectangular pulse. The functions that I need to find the fast Fourier transform of are shown below and they need to be plotted in a graph. I need to use the equations listed here. Please kindly show me the Matlab code to be used for each function since each function is a specific case and each needs its own code. The x-axis should be the frequency and the y-axis should be the magnitude. The "abs" indicates we take the absolute value of the function. The "exp" indicates we take the exponential "e" which is approximately 2.718281828 and we raise it to a power with the function specified below. The plot of the Fast Fourier Transform needs to have converted the function within the time range of -5 to 5 seconds into the corresponding frequencies. The functions that I need to find the Fast Fourier Transform of are shown below. The Fast Fourier Transforms need to be plotted in a graph are:

The sign signal: y=sgn(t) where y=(-1) from t=negative infinity to 0, y=0 when t=0, and y=1 from t=zero to positive infinity. The time range "t" is from -5 to 5 seconds where -5<=t<=5 seconds. The Fast Fourier Transform needs to have converted the function from the time range of -5 to 5 seconds into its corresponding frequencies. The Fast Fourier Transform of this function needs to be plotted in a graph.

The Triangle Signal: y=1-((2*(abs(t)))/tau) where tau=2, and "t" for time is within (-tau/2,tau/2) and the time range "t" is from -5<=t<=5 seconds. The Fast Fourier Transform of this function needs to have the time range of -5 to 5 seconds converted to its corresponding frequencies. The Fast Fourier Transform of this function needs to be plotted in a graph.

The bilateral exponential signal: y=exp(-abs(t)) where "t" is the time which ranges from -5 to 5 seconds and can also be written as -5<=t<=5 seconds. The Fast Fourier Transform needs to have the time range of -5 to 5 seconds converted to its corresponding frequencies. The Fast Fourier Transform of this function needs to be plotted in a graph.

The Rectangular Pulse: I need to find the Fast Fourier transform of the rectangular pulse with these different widths of the rectangular pulse with widths of width=0.05,width=0.1,width=0.5, width=1, width=5. The rectangular pulse for all of these widths need to be centered at x=0 when taking the Fast Fourier Transform. The Fast Fourier Transform of this function needs to be plotted in a graph. This function only does not have a time range only a width.

The Gaussian Signal: y=exp((-(t-c)^2)/(2*(sigma^2)) where c=0 and sigma=0.5. The time range "t" is from -5 to 5 seconds where -5<=t<=5 seconds. The Fast Fourier Transform needs to have converted its time range of -5 to 5 seconds to its corresponding frequencies. The Fast Fourier Transform of this function needs to be plotted in a graph.

All of these functions need to have their Fast Fourier Transform Plotted in a Matlab Graph. The x-axis should be the frequency and the y-axis should be the magnitude. I have to use the Fast Fourier Transform Function in Matlab which is fft(function). The magnitude needs to be plotted in a graph by also taking the absolute value of the Fast Fourier Transform. It needs to use abs(fft(function)). I can not use the regular Fourier Transform. Please kindly show me the Matlab code that is to be used for each of these functions since each function is a specific case and each needs its own code.

Thank you.

Sincerely,

S.S.K