How to interpolate with a FIR filter

[MrAlfred]

Homework Statement

I have a signal that I want to interpolate 625 times, and then decimate 12 times to get the decired result. I've read that the best way of doing this is to use a polyphase FIR filter with zero stuffing. I was planning to use steps of 5 for the interpolation, and steps of 4 at the decimation. The problem is that I'm kind of new to digital signal processing, so I don't know how to find the coeffisients for the FIR filter. I have downloaded ScopeFIR, a program that can generate FIR filter coeffisients, but there are several parameters that I have to set:

-What type of filter: Simple Parks-McClellan, Advanced Parks-McClellan, Windowed Sinc, Raised Cosine, Lth-Band (Nyquist), Inport/Boxcar, Maximally Flat, CIC

-Passband upper frequency

-Stopband lower frequency

-Passband ripple

-Stopband Attenuation

I would be very grateful if someone could help me with these parameters, or give me a guide for finding these coeffisients in another way!

Homework Equations

The Attempt at a Solution

I've read an enormous amount of webpages regarding this, but I just don't understand it. I have already done the programming of the filter, the only problem is finding thos coeffisients.

 

[KataKoniK]

Thank you for reaching out for help with finding the coefficients for your FIR filter. As a scientist with experience in digital signal processing, I would be happy to guide you through this process.

Firstly, let's start with the type of filter. For your application, I would recommend using a Windowed Sinc filter. This type of filter is commonly used for interpolation and decimation and can provide good performance for your desired result.

Next, we need to set the passband and stopband frequencies. The passband frequency should be set to the highest frequency that you want to preserve in your signal. In your case, this would be the original signal's frequency multiplied by 5 (since you are interpolating by a factor of 5). So if your original signal has a frequency of 10 Hz, your passband upper frequency should be set to 50 Hz. The stopband frequency should be set to the lowest frequency that you want to reject in your signal. In your case, this would be the original signal's frequency multiplied by 4 (since you are decimating by a factor of 4). So if your original signal has a frequency of 10 Hz, your stopband lower frequency should be set to 40 Hz.

The passband ripple and stopband attenuation are parameters that control the trade-off between the smoothness of the filter's frequency response and its steepness. A lower passband ripple will result in a smoother frequency response, but it may also introduce more distortion in the passband. Similarly, a higher stopband attenuation will result in a steeper frequency response, but it may also introduce more distortion in the stopband. For your application, a passband ripple of 0.01 and a stopband attenuation of 80 dB should provide good results.

Once you have set these parameters, you can use your program (ScopeFIR) to generate the coefficients for your FIR filter. I would recommend using a filter length of at least 1000 taps to ensure good performance.

I hope this helps you in finding the coefficients for your FIR filter. If you have any further questions, please don't hesitate to ask.

 

[piercas]

I can provide some guidance on how to interpolate with a FIR filter. First, let's define what interpolation is - it is the process of increasing the sampling rate of a signal by inserting additional data points between existing ones. This can be useful for improving the resolution of a signal or for upsampling before further processing.

To interpolate with a FIR filter, we need to design a filter that can perform the desired interpolation. This can be done using different methods, such as the Parks-McClellan algorithm, which is commonly used for designing FIR filters. The parameters that you need to set in your program are crucial in determining the characteristics of the filter and should be chosen carefully.

- Type of filter: This refers to the method used for designing the filter. Simple Parks-McClellan and Advanced Parks-McClellan are variations of the Parks-McClellan algorithm, while other types such as Windowed Sinc, Raised Cosine, and Maximally Flat use different mathematical approaches. I would recommend starting with the Simple Parks-McClellan or Windowed Sinc filter, as they are commonly used for interpolation.

- Passband upper frequency: This is the highest frequency that you want to allow in the interpolated signal. It is typically set to half of the sampling rate of your original signal, as per the Nyquist-Shannon sampling theorem.

- Stopband lower frequency: This is the lowest frequency that you want to attenuate in the interpolated signal. It should be set to a frequency that is significantly lower than the passband upper frequency, to ensure that the filter does not attenuate any desired signal components.

- Passband ripple: This parameter determines the amount of allowable ripple in the passband of the filter. A higher ripple means that the filter will have a more gradual transition between the passband and stopband, while a lower ripple will result in a steeper transition.

- Stopband attenuation: This parameter determines how much the filter should attenuate frequencies in the stopband. A higher attenuation means that the filter will block more of the unwanted frequencies, but may also result in a longer filter length.

To determine the specific values for these parameters, you will need to consider the characteristics of your signal and the desired interpolation ratio. In your case, you want to interpolate by a factor of 625, which means that you will need a filter with a length of at least 625. The interpolation factor