How to get magnitude and phase onfo of a given signal (2024)

FAQs

How to get the magnitude and phase of a signal? ›

The magnitude is the square root of the sum of the squares of the real and imaginary parts. The phase is relative to the start of the time record or relative to a single-cycle cosine wave starting at the beginning of the time record. Single-channel phase measurements are stable only if the input signal is triggered.

A geometric way to obtain approximate magnitude and phase frequency responses is using the effects of zeros and poles on the frequency response of an LTI system. G ( s ) | s = j Ω 0 = K j Ω 0 − z j Ω 0 − p = K Z → ( Ω 0 ) P → ( Ω 0 ) .

Phase can be measured in distance, time, or degrees. If the peaks of two signals with the same frequency are in exact alignment at the same time, they are said to be in phase. Conversely, if the peaks of two signals with the same frequency are not in exact alignment at the same time, they are said to be out of phase.”

To obtain the phase response, we take the arctan of the numerator, and subtract from it the arctan of the denominator. (Angle of a complex number expressed as a vector is something you may not be familiar with.

The magnitude describes the strength of each frequency in the signal. The phase describes the sine/cosine phase of each frequency. The phase can also be thought of as the relative proportion of sines and cosines in the signal (i.e., a phase of zero contains only cosines and a phase of 90 degrees contains only sines).

The time interval for 1° of phase is inversely proportional to the frequency. If the frequency of a signal is given by f, then the time t_deg (in seconds) corresponding to 1° of phase is t_deg = 1 / (360f) = T / 360. Therefore, a 1° phase shift on a 5 MHz signal corresponds to a time shift of 555 picoseconds.

Impedance in circuits

This is less mathematical and requires an appreciation that a sinusoidal curve can be constructed by a rotating vector arrow (seen in SHM), and a knowledge of Pythagoras. Here Z0​ is the magnitude of Z so Z0​=X2+Y2 ​ and ϕ is the phase of Z which has the value ϕ=arctan(XY​).

The phase of a wave is the value representing a fraction of a wave cycle. In a wave, a complete cycle, from crest to crest or trough to trough, is equal to 2π [rad]. Every fraction of that length, therefore, is less than 2π [rad]. Half a cycle is π [rad], while a quarter of a cycle is π/2 [rad].

The phase shift equation is ps = 360 * td / p, where ps is the phase shift in degrees, td is the time difference between waves and p is the wave period. Continuing the example, 360 * -0.001 / 0.01 gives a phase shift of -36 degrees.

In Mathematics, face value is the actual value of the digit in a number. For example, if 567 is a number, then the face value of 6 is 6 only, whereas its place value is tens (i.e. 60). Thus, for any number, having a two-digit, three-digit or 'n' number of digits, every digit will have a place value and a face value.

How do you find the phase of an equation? ›

A phase shift is when a graph is moved horizontally to the left or right a specific number of units. It can be found by using the general formula of transformations y = A f ( B x − C ) + D and identifying the B and C values.

A transfer function, H(ω), has a magnitude response |H(ω)| and a phase response ϕ(ω) such that H(ω) = |H(ω)| e^iϕ(ω). The only difference between a complex number z and a transfer function H(ω) is z is one complex number whereas H(ω) is an entire function of complex numbers: a complex number for each frequency value ω.

The magnitude tells you the strength of the frequency components relative to other components. The phase tells you how all the frequency components align in time. Plot the magnitude and the phase components of the frequency spectrum of the signal. The magnitude is conveniently plotted in a logarithmic scale (dB).

In signal processing, phase response is the relationship between the phase of a sinusoidal input and the output signal passing through any device that accepts input and produces an output signal, such as an amplifier or a filter.

Finding the amplitude, period, and phase shift of a function of the form A × sin(Bx - C) + D or A × cos(Bx - C) + D goes as follows: The amplitude is equal to A ; The period is equal to 2π / B ; and. The phase shift is equal to C / B .

To calculate the phase angle, one typically measures the time difference between corresponding points on the voltage and current waveforms, then converts this time delay into an angle using the formula: phase angle = (time delay / period) * 360 degrees.