Frequency Domain Analysis Flashcards
Which part of a discrete fourier series is real?
Even - Cosine part
Which part of a discrete fourier sries is Imaginary?
Odd - Sine
Describe what the spectra of a periodic series is….
It is where a fourier series calculation is performed on a signal. There is a formula that is used to represent the calculaiton. The table method can be used to seperate the real and imaginary part to calulate the solution. The answer is represented by ak and ai and can be split into ints magnitude and its phase
What is the symbol representation of the imaginary and real part of a fourier series
ak = real ai = imaginary
Name the mthod of solving a fourier series and briefly describe it
Tablular method. This is where you take each calculation of each element in the series (k substittions) and seperate it into its imaginary and real parts.
What effect does using a unit step function have on a fourier series calculation
it means that the sum is used to calculate the series rather than just an impulse each element it caluclated individually.
which conditions are a fourier series used as a calculation
frequency analysis on the point where the data is represented as a periodic series (i.e cosine, sines etc… repeating itself etc…)
Describe the magnitude of a fourier series
the square root of the (real part squared + the imaginary part squared)
describe the phase of the fourier series
arctan of the real part divided by the imaginary part
NAme the 6 properties of a fourier series
Linearity time shifting differentiation integration circular convolution modulation
describe what linearity is
The sum of two weights (elements) is equal to the addition of each of the respective weights (elements)
time shifting is..
defines the effect of shifting x[n] by n0 at sampling intevals. it changes the phase (moves it along) but not the magnitude
differentiation
Used to estimate the slope of sigma
integration
running sum of x[n]. only period if x[n] has zero averages
circular convolution
over one period it ensures the convergence of the summation It also shows that time domain convolution is equal to the frequency domain multiplication
Formula for a spectra of periodic series in a fourier series
Describe a table where the tabular method has been used to solve a fourier series
Formula for calculating the phase and magnitude of a FS
Derive FT part 1:
FT derive part 2:
FT derive part 3:
FT derive par t4:
Draw the mathematical descriptions of the properties of the fourier transform…
how does the fourier transform with the frequency domain map to the time domain?
What are the equations that map from frequency domain to time domain within the foruier tranform.
How do you calulcate the frequency response H(omega) - graphic formula
discrete to fourier graph…
Fourier series table…
operation | periodic signal | discrete fourier series | - 9 rows
The fourier transform of aperiodic signals : properties and pairs:
properties: operation | signal | FT | - 7 rows
pairs - | waveform | signal | spectrum X(omega) | - 5 rows
