Amplitude distortion and phase distortion

It is the will of Bode.

Go read "Network Analysis and Feedback Amplifier Design", H. W. Bode

I have read that a Fir filter has linear phase so is amplitude response hasn't distortion in passband(no oscillation is present):this affirmation is true? bye

homework problem?

Mark

By phase distortion, I assume you are referring to a deviation from linear phase. There is a relationship, but it depends on the transfer function of the system. For example, an all-pass filter has an output whose amplitude does not vary with frequency, but its phase shift does.

Joseph, A FIR filter can be made to have linear phase. Any FIR filter whose coefficents are symmetrical with respect to the center coefficent wil have linear phase. For example, let A(c) = the coefficient of the middle sample. Then if A(c-1) = A(c+1), A(c-2) = A(c+2), etc the filter will have linear phase. All FIRs do not necessarily have linear phase. No analog system can be made to have linear phase. Regards, Kral

The term distortion is not really used in enginerring. In signal theory, there is the linear transmission function, which doe not creates harmonics, and there are the non-linear cases with harmonics. The linear transmission function relates the amplitude and phase response of the system to the input signal. The non-linear cases are not nearly as good covered with theory as are the linear ones.

Rene

No.

Cheers! Rich

Not all FIR filters have a linear phase vs frequency relationship.

If a linear phase vs frequency relationship is required it is usual to use a FIR.

A filter with a linear linear phase vs frequency relationship delays a time domain signal without changing its shape. The delayed signal will be distorted if it has harmonic content that lies outside the range of frequencies where the linear phase relationship is true.

Charles

To start with, get rid of this distortion stuff. Linear systems do not have distortions, by definition. When distortion comes in, they are in the nonlinear regime, eg clipping. This is not covered by the linear theory.

There is amplitude ratio and phase shift. One pair for each frequency.

A FIR is a forward propagating multiply-add-register set. It has thus a finit impulse response. Depending on the coefficient, whatever amplitude and phase response can be achieved.

Rene

Analog low pass Bessel filters can have a good approximation to linear phase. A piece of transmission line also has excellent linear phase.

C.

If you are only talking about waveform distortion, this is true.

The terms 'phase distortion' and 'frequency distortion' (meaning limited bandwidth) also exist. These days they are less commonly used expressions, but they do need to be excluded from your definition.

There seem to be different meanings of 'linear phase' if used by digital and analog guys respectivly. In digital is meant a filter without any phase shift (exept a certain unavoidable constant delay). An analog guy will understand 'linear phase', that the phase is increasing linearly with frequency. Unadvertedly this will lead to the same as above, a constant delay for all frequencies. The thing is, the digital guy forgets about the delay and is proud that his filter has no phase change at all. And the analog guy forgets about the filter and concentrates on the delay... The analog loves OTOH a *minimum* phase filter. This type is related to the OP-question, because in the analog world every filter needs a phase change to perform its function. For a filter of 1st order this will be +90° for a HP or -90° for a LP at the -3dB points and +/-180° at infinite/zero. A 2nd order filter has double of these values. Most natural processes (pendulum, mass/spring etc.) behave as minimum phase systems. A minimum phase filter has the shortest possible delay. Sometimes a very important attribute. We can calculate the phase from the amplitude in a frequency plot for a minimum phase system, this might be helpful in certain processing situations.

a 1st order filter has 45° at the corner frequency and 90° at infinite, what I wrote was for a second order filter. sorry

and

check a good filter book. linear phase = constant delay delay is the derivative of phase

Yes, exactly what I wrote. For a digital guy the meaning is not constant delay, but a filter with an amplitude function without any impact on the phase. This is indeed impossible in the analog domain.