Working with the Fourier Transform Derivation.

An electrical signal comprises a single triangular pulse, as shown in Figure A4 as a function f(t) against time t. Derive the Fourier transform of the pulse. Sketch F(w) giving the positions of the points at which F(w)=0 and the magnitude of F(0).

Fourier analysis

(a) Explain the relationship between the spectral components indicated above and the corresponding graph showing the motion of the surface of the motor plotted as a function of time. What do they represent? (b) Given the amplitudes indicated in the above diagram, copy and complete the table below for the amplitude of the vibration in the time domain. Sketch the result of your reconstructed waveform in the period 0 < t < 0.1 ms, assuming f0 = 5000 Hz. See attached file for full problem description.

Find the Fourier series, sketch the graph of the function for 3 periods.

Please see the attached file for the fully formatted function. Find the Fourier series, sketch the graph of the function for 3 periods. Is this a discontinuous graph? Is it an even or odd function, I know there are Fourier series rules for them.

Fourier Transform of a Normal Gaussian curve - 3 PARTS!!!

1) if f(x) is a Gaussian with unit area - show that the scaled and stretched function 1/a * f(x/a) also has unit area - that's the hardest part. The other parts (along with a detailed explanation of this one) are in an attachment as both mathcad v.11 and in an html file - they're the same thing - but if you don't have mathcad you CAN see the html file.. just extract it to your desktop and click the .htm file... Thanks!!!

Fourier series

Please see attachment.