week 8

Question 1

Fourier Series Theorum

Answer 1

any periodic signal can be represented by a sum of sinusoids

Question 2

what do sinusoids have at the frequency of each wave? (1st property)

Answer 2

energy!

Question 3

3 parameters of sinusoids? (2nd property)

Answer 3

amplitude, phase, frequency

Question 4

what can periodic signals be decomposed into? (3rd property, Fourier Series Theorem)

Answer 4

equivalent sinusoidal waves

Question 5

you can find some combination of ______________ sinusoids that can be added to reconstruct any period signal (4th property)

Answer 5

harmonically related

Question 6

sinusoid representation of signal waves work in __________ (5th property)

Answer 6

both directions

Question 7

sinusoids are best represented in the ______ domain (6th property)

Answer 7

frequency

Question 8

________ can change the magnitude and phase of sinusoid (8th property)

Answer 8

calculus operations

Question 9

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)

Answer 9

same

Question 10

harmonically related sinusoids are orthogonal, periodic decomposition of components are ______ (10th property)

Answer 10

independent

Question 11

are biological signals periodic?

Answer 11

no but they can be taken as such for analysis purposes

Question 12

period of X(t) is

Answer 12

T

Question 13

base fundamental frequency is

Answer 13

f1 = 1/T

Question 14

the ____ sinusoids in summation, the better the representation of the signal (x(t))

Answer 14

more

Question 15

Fourier series in Matlab

Answer 15

Xf = fft(x)

Question 16

what are the inputs and output of
Xf = fft(x)

Answer 16

x is the input waveform
Xf is a complex vector with sinusoid coefficients (first term is real unnormalized DC component)

Question 17

magnitude of frequency spectra

Answer 17

abs(Xf)

Question 18

phase of spectra

Answer 18

angle(Xf)

Question 19

bandwidth

Answer 19

range of frequency domain

Question 20

filters in frequency domain

Answer 20

target is to reduce noise by limiting bandwidth to the range of interest

Question 21

filter properties

Answer 21

filter type, bandwidth, attenuation slope

Question 22

pass band

Answer 22

input signal in the desired range is passed to output without change

Question 23

stop band

Answer 23

amplitude of signals in this range ideally reduced to 0

Question 24

filtering: the value you want to multiply depends on…

Answer 24

the instantaneous frequency

*1 to frequency you want to keep/pass
*0 to frequency you want to discard/stop

Question 25

cut-off frequency

Answer 25

frequency between the pass and stop band