The Fourier transform

In-class group activity 5

Find the Fourier transform of a wave pulse

Consider a wave pulse y(x, t) at t = 0.  If we want to build this wave pulse by superimposing harmonic waves, we need waves with many different wave numbers k = 2π/λ or wavelength λ.  Excel has a Fourier transform function.  Given a pulse y(x), Excel calculates the amplitudes of the sine and cosine waves that are needed to synthesize this pulse.  These amplitudes as a function wave numbers k = 2π/λ are the magnitude of the Fourier transform of the pulse y(x).

Open a Microsoft Word document to keep a log of your results and discussions.

Click here to examine the plots of four wave pulses and the magnitudes of the corresponding Fourier transforms calculated using Excel.

pulse

x
(m)

k
(1/m)

product
x k

1

 

 

 

2

 

 

 

3

 

 

 

4

 

 

 

 


What have we learned?