Hey Guys,

Quick question from a book I'm reading. The book states that with a Bessel filter "the linear phase shift for all frequencies in the passband means that the fundamental frequency and harmonics of a nonsinusoidal input signal with shift linearly in phase as the pass through the filter."

Why does the signal have to be nonsinudoidal?

Thanks in advance for any help,

Austin

 

It's not that it has to be, it's just that filters are used on non-sinusoidal signals. Sinusoids have no harmonics.

 

Technically a sinusoid is a single frequency signal and there's generally no reason to filter a single frequency. Music, for example, is made up of many different sinusoidal frequencies as determined by a Fourier analysis but the combined signal is considered non-sinusoidal. Filters are used to remove undesired signals from such a non-sinusoid.

 

Music, for example, is made up of many different sinusoidal frequencies as determined by a Fourier analysis but the combined signal is considered non-sinusoidal.

At the risk of confusing the OP and derailing the topic, I have to argue that reality is the exact opposite of this statement. Real-world signals are not a bunch of sinusoids together that assemble various regular waveforms. The opposite is true; real-world signals are what they are, and they can be modeled, or constructed, by adding a bunch of sinusoids together. Excepting additive synthesizers, real-world signals are not built from added sinusoids, they're described by innumerable other functions. In the world of math and theory it may not make any difference, but I think it's important not to confuse those who may be new. Fourier theory can be confusing.

 

At the risk of confusing the OP and derailing the topic, I have to argue that reality is the exact opposite of this statement. Real-world signals are not a bunch of sinusoids together that assemble various regular waveforms. The opposite is true; real-world signals are what they are, and they can be modeled, or constructed, by adding a bunch of sinusoids together. Excepting additive synthesizers, real-world signals are not built from added sinusoids, they're described by innumerable other functions. In the world of math and theory it may not make any difference, but I think it's important not to confuse those who may be new. Fourier theory can be confusing.

Perhaps. But a filter will suppress those mathematical sinusiods outside its passband in a music waveform and pass those in the passband. How would you explain that without using Fourier analysis?

And real world waveforms may not be generated by combining sinusoids but they can be mostly described by the sinusoids of Fourier analysis (except for some ideal waveshapes, such as perfect square-waves). I don't know what "innumerable other functions" you are referring to.