;PURPOSE:
;	The purpose of this script is to show the effect of sampling a function
;	on its fft
pro fft_sample_region

!p.multi=[0,2,2]

;Set up Quantitities necessary for FFT and real signal
DeltaX=1.		;Spacing in the Time Domain (sec) or Spatial Domain (m)
Period1=10.			;Period of First Signal
Period2=22.			;Period of Second Signal
Strength1=20.			;Strength of First Signal
Strength2=80.			;Strength of Second Signal
SignalN=1000.			;Number of Sample Points
SignalLength=SignalN*DeltaX	;Total Length in Time (or Space)
FreqSpacing=1/(SignalLength)	;In Frequency Domain, Spacing is 1/Length
KMax1=SignalN/2		;The index of the Frequency Split (Positive/Negative)


;Here is the Signal
x=DeltaX*findgen(SignalN)
y1=Strength1*sin((2*!pi/Period1)*x)+Strength2*cos((2*!pi/Period2)*x)
plot,x,y1

FreqSpacing1=1/(SignalLength)
Kvals1=FreqSpacing1*(-KMax1+findgen(SignalN))
FftY1=fft(y1)
plot,KVals1,abs(shift(ffty1,KMax1))^2


;Now Sample the function and see what we get Sample=y2
SampleSignalN=N_elements(y1)/2
SampleSignalLength=SampleSignalN*DeltaX
FreqSpacing2=1/(SampleSignalLength)
KMax2=SampleSignalN/2
Kvals2=FreqSpacing2*(-KMax2+findgen(SampleSignalN))

;Here is the sampled signal
x=DeltaX*findgen(SampleSignalN)
y2=y1(0:SampleSignalN)
plot,x,y2

FftY2=fft(Y2)
plot,KVals2,abs(shift(ffty2,KMax2))^2

end