lab week 6 Flashcards
amplitude
the difference between the maximum values to the baseline value
period
of a wave is time it takes to finish the complete cycle, in the figure, we can see that the period can be measured from the two adjacent peaks
wavelength
the distance between two successive crests (гребни) or troughs (низшая точка) of a wave
frequency
the number of waves that pass a fixed place in a given amount of time. e. g. how many cycles pass within 1 second.
the unit of frequency is cycles/second, or Hertz (abbreviated Hz).
Frequency is different from period, but they are related to each other:
sampling, sampling rate
discretization points we did both in time and space (blue dots on the graphs). Only at these dots, we have sampled the value of the wave. Usually when we record a wave, we need to specify how often we sample the wave in time - sampling rate
if we sample a wave at 2 Hz, it means that every second we sample two data points
what’s that?
angular frequency
specifies how many cycles occur in a second, in radians per second
time domain signal vs frequency domain
discrete Fourier transform
DFT
can transform a sequence of evenly spaced signal to the information about the frequency of all the sine waves that needed to sum to the time domain signal. It is defined as:
The amplitudes returned by DFT equal to…
…the amplitudes of the signals fed into the DFT if we normalize it by the number of sample points
DFT in code
FFT
Fast Fourier Transform (FFT) is an efficient algorithm to calculate the DFT of a sequence
It is described first in Cooley and Tukey’s classic paper in 1965, but the idea actually can be traced back to Gauss’s unpublished work in 1805. It is a divide and conquer algorithm that recursively breaks the DFT into smaller DFTs to bring down the computation
TFR
Time-frequency representation
X-axis: time
Y-axis: frequency
Colour: spectral power i.e. Fourier Coefficient
define N_samples_FFT as the number of samples you need for your FFT
int(srate/freq_res)
sampling rate over frequency resolution
