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amaresh92
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how a step function has frequency content in it?
thanks
thanks
IS it true that a function varies from +2 to +4 also has frequency component in it.sophiecentaur said:There is a mathematical 'reason': Any signal / waveform / function that varies in time (time domain) can be transformed to a function in the 'frequency domain', which shows its frequency spectrum.
sophiecentaur said:It's more an identity than a 'truth'. It's down to the definitions of time and frequency domain. Any time varying function can be described in the frequency domain and vice versa.
A good intuitive exercise could be to grab a few of the first harmonics mentioned in post #2 and try to build the step function from scratch and see how the 'squareness' develops.amaresh92 said:how a step function has frequency content in it?
gnurf said:A good intuitive exercise could be to grab a few of the first harmonics mentioned in post #2 and try to build the step function from scratch and see how the 'squareness' develops.
You're right of course. I actually replaced 'square wave' with 'step function' before submitting when I discovered I wasn't answering his question. That was never going to work very well I guess. Thanks for keeping the place tidy.sophiecentaur said:Being picky, I would point out that a "unit step signal" is not a "square wave". A unit step function is zero for all time before until it changes value. Thereafter, it is 1, for the rest of all time. There are no 'harmonics' because there is no 'repeat' and the 'fundamental' has zero frequency.
It is a very idealised function and, as its (infinite) energy is spread over an infinite number of frequency components of infinitessimally small value.
A unit step signal is a function in Fourier analysis that has a value of 1 for all positive values of time and a value of 0 for all negative values of time. It is often used as a basic building block for more complex signals in Fourier analysis.
The Fourier transform of a unit step signal is different from other signals because it has a discontinuity at time 0. This means that the Fourier transform will have a constant magnitude for all frequencies, rather than a varying magnitude like other signals.
The formula for the Fourier transform of a unit step signal is F(w) = 1/(jw) + πδ(w), where j is the imaginary unit, w is the frequency, and δ(w) is the Dirac delta function.
The Fourier transform of a unit step signal is used in practical applications to analyze the frequency content of signals. It can also be used to filter out specific frequencies or to reconstruct a signal from its frequency components.
One limitation of using the Fourier transform of a unit step signal is that it assumes the signal is infinite in duration. This may not always be the case in practical applications, so other techniques may need to be used. Additionally, the Fourier transform may not accurately represent signals with sharp changes or discontinuities.