# how can I design Chebyshev filter with 5th-order polynomial and 0.001%-allowed ripples?

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

• 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. – Matt L. Jan 18 '19 at 14:06
• Thanks for your reply. Yes I'm talking about digital filter. That I'm talking about I can't understand what did he mean – Mahmoud Kamal Elshazly Jan 18 '19 at 14:10
• Could you link to the paper you refer to? – Matt L. Jan 18 '19 at 14:12
• You can use the function cheby1 from the signal processing toolbox. – Matt L. Jan 18 '19 at 14:13
• apps.dtic.mil/dtic/tr/fulltext/u2/1035578.pdf – Mahmoud Kamal Elshazly Jan 18 '19 at 14:15

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 $$\delta=0.0001$$.

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