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I'm very beginner in signal processing. I need to design a Chebyshev filter with 5th-order polynomial and 0.001%-allowed ripples by using matlab as I found in a paper. I'm filtering pressure data inside combustion engine. In matlab I've to define normalized passband edge frequency and peak-to-peak passband ripple. I don't know what did the paper's author mean by 0.001% allowed ripples?

Any help would be appreciated

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    $\begingroup$ I suppose you're talking about a digital filter. Are you sure they meant $0.001$ percent? I would guess it's a ripple size of $0.001$, which for an ideal passband response of unity corresponds to a $0.1$ percent maximum deviation. $\endgroup$ – Matt L. Jan 18 '19 at 14:06
  • $\begingroup$ Thanks for your reply. Yes I'm talking about digital filter. That I'm talking about I can't understand what did he mean $\endgroup$ – Mahmoud Kamal Elshazly Jan 18 '19 at 14:10
  • $\begingroup$ Could you link to the paper you refer to? $\endgroup$ – Matt L. Jan 18 '19 at 14:12
  • $\begingroup$ You can use the function cheby1 from the signal processing toolbox. $\endgroup$ – Matt L. Jan 18 '19 at 14:13
  • $\begingroup$ apps.dtic.mil/dtic/tr/fulltext/u2/1035578.pdf $\endgroup$ – Mahmoud Kamal Elshazly Jan 18 '19 at 14:15
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A type I Chebyshev filter has a passband magnitude response oscillating between the values $1$ and $1-\delta$, where $\delta$ is the maximum passband approximation error. The Matlab function $\tt{cheby1}$ requires the desired passband ripple in dB:

$$R_p=20\log\left(\frac{1}{1-\delta}\right)$$

The normalized cut-off frequency is

$$\omega_c=2\pi\frac{f_c}{f_s}$$

where $f_c$ is the cut-off frequency in Hertz, and $f_s$ is the sampling frequency in Hertz. The input parameter $\tt{Wc}$ required by $\tt{cheby1}$ is equal to $\omega_c/\pi$.

I don't think that the authors of the paper you refer to got the percentages right. A tip: for a "ripple percentage" of $0.001$ try $\delta=0.0001$.

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  • $\begingroup$ Thank u so much dr Matt now that make a sense for me $\endgroup$ – Mahmoud Kamal Elshazly Jan 20 '19 at 20:24

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