Magnitude and Phase of Complex Number
Create a complex number, and compute its magnitude and phase.
z = 2*exp(i*0.5)
z = 1.7552 + 0.9589i
r = abs(z)
r = 2
theta = angle(z)
theta = 0.5000
Create a signal that consists of two sinusoids of frequencies 15 Hz and 40 Hz. The first sinusoid has a phase of , and the second has a phase of . Sample the signal at 100 Hz for one second.
fs = 100; t = 0:1/fs:1-1/fs; x = cos(2*pi*15*t - pi/4) - sin(2*pi*40*t);
Compute the Fourier transform of the signal. Plot the magnitude of the transform as a function of frequency.
y = fft(x); z = fftshift(y); ly = length(y); f = (-ly/2:ly/2-1)/ly*fs; stem(f,abs(z)) xlabel 'Frequency (Hz)' ylabel '|y|' grid
Compute the phase of the transform, removing small-magnitude transform values. Plot the phase as a function of frequency.
tol = 1e-6; z(abs(z) < tol) = 0; theta = angle(z); stem(f,theta/pi) xlabel 'Frequency (Hz)' ylabel 'Phase / \pi' grid
z — Input array
scalar | vector | matrix | multidimensional array
Input array, specified as a scalar, vector, matrix, or multidimensional array. When
the elements of
z are non-negative real numbers,
angle returns 0. When the elements of
negative real numbers,
angle returns π.
Complex Number Support: Yes
angle takes a complex number z = x +
iy and uses the
atan2 function to compute the angle between
the positive x-axis and a ray from the origin to the point
(x,y) in the xy-plane.
Calculate with arrays that have more rows than fit in memory.
This function fully supports tall arrays. For more information, see Tall Arrays.
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This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.
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This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).
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This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).