week 8 Flashcards
Fourier Series Theorum
any periodic signal can be represented by a sum of sinusoids
what do sinusoids have at the frequency of each wave? (1st property)
energy!
3 parameters of sinusoids? (2nd property)
amplitude, phase, frequency
what can periodic signals be decomposed into? (3rd property, Fourier Series Theorem)
equivalent sinusoidal waves
you can find some combination of ______________ sinusoids that can be added to reconstruct any period signal (4th property)
harmonically related
sinusoid representation of signal waves work in __________ (5th property)
both directions
sinusoids are best represented in the ______ domain (6th property)
frequency
________ can change the magnitude and phase of sinusoid (8th property)
calculus operations
if input to linear signal is a sinusoid then the output is a sinusoid at the ____ frequency, only changes are to magnitude and phase (9th property)
same
harmonically related sinusoids are orthogonal, periodic decomposition of components are ______ (10th property)
independent
are biological signals periodic?
no but they can be taken as such for analysis purposes
period of X(t) is
T
base fundamental frequency is
f1 = 1/T
the ____ sinusoids in summation, the better the representation of the signal (x(t))
more
Fourier series in Matlab
Xf = fft(x)
what are the inputs and output of
Xf = fft(x)
x is the input waveform
Xf is a complex vector with sinusoid coefficients (first term is real unnormalized DC component)
magnitude of frequency spectra
abs(Xf)
phase of spectra
angle(Xf)
bandwidth
range of frequency domain
filters in frequency domain
target is to reduce noise by limiting bandwidth to the range of interest
filter properties
filter type, bandwidth, attenuation slope
pass band
input signal in the desired range is passed to output without change
stop band
amplitude of signals in this range ideally reduced to 0
filtering: the value you want to multiply depends on…
the instantaneous frequency
*1 to frequency you want to keep/pass
*0 to frequency you want to discard/stop
cut-off frequency
frequency between the pass and stop band
