I deal with a signal of sampling frequency of 48000 Hz.
I do not need this much and doing decimation in order to get to 8000 Hz, so, decimation of 6-th order.
Additionally, I know I need to filter out 50 Hz and its harmonics. I am going to do it with the help of FFT-iFFT procedure, as I really do not know how to design a FIR filter with all its zeros and poles...
My question is:
Shall I filter out harmonics before decimating, or I can do it later?
Because if I need to filter out harmonics before, its gonna be insane to filter out 24000/50=480 of harmonics, and after decimating the computational memory decreases times (4000/50=80)!
Related
I am trying to design a FIR bandpass filter to reject middle frequencies of a signal using fiterDesigner tool. However I have never used this before so I had some troubles but I know the basic idea of the bandpass filter.
and here is my fftshift(fft(signal)) output (only fs/2 part):
My sampling frequency value is 44100. I need to reject middle frequency. So I set up filter design as above picture. (Filter Order should be minimum order).
When I try to design this filter, I got:
Fpass2 must be less than 22050 (half of sampling frequency).
I could not get why this happened. How can I design a FIR bandpass filter to reject the middle frequency of a signal?
In digital signal processing, the rule of thumb is that any processing frequency must be less than the half of the sampling frequency. Look a the Nyquist criterion somewhere, for example here: https://en.wikipedia.org/wiki/Nyquist–Shannon_sampling_theorem.
As you can see, there is a good portion of math involved. In a nutshell, if the frequency is more than the half of the sampling frequency, there will be overlapping of the spectrum around half. The solution is to either increase sampling frequency, which I probably not possible, or to reduce the filter design frequencies.
I have a quick question on sensor data decimation, which I'm sure is pretty easy but thought I'd check. I have a sensor that is sampling at 25Hz and the data is being sent across a serial RS232 connection to an external data logger, which is logging the data at 10Hz.
I think if I want to recover a true 10Hz signal, I should I pass the original 25 Hz signal through a decimation process (i.e. filtering followed by down sampling). Is this correct?
If it is correct, I was thinking that I should decimate the original 25Hz signal by passing it through a low pass filter with a cutoff frequency of ~10 Hz, to remove the higher frequency components. The filtered signal would then be down sampled to produce a final signal. This down sampling would be achieved by extracting a value every 2.5 samples from the filtered signal.
So in other words, the 1st value of the final signal would be the first sample of the filtered signal. The second value of the final signal would be the average of samples 2 & 3 from the filtered signal. Then the third value of the final signal would be sample 5 from the filtered signal, and the fourth sample would be an average between samples 7 & 8 etc.....
Hopefully that makes sense. I think that would provide me with a clean 10Hz signal.
Many thanks for your time and efforts on this, they are very much appreciated
Cheers
The type of filtering you should use will depend in part on what you are using this signal for and how noisy the captured data is.
In general, you should not change the sampling frequency of the filter constantly, this could introduce artificial periodic noise in the captured data. My guess is that for this process you are sampling something that doesn't change rapidly. You might want to just take a rolling average of the last 3 samples, even though some of the data averaged into each logged sample will overlap.
I have a signal that may not be periodic. We take about 15secs worth of samples (# 10kHz sampling rate) and we need to do the FFT on that signal to get the frequency content.
The problem is that we are implementing this FFT on an embedded system (DSP) which provides a library FFT of max. 1024 length. That is, it takes in 1024 data points as input and provides a 1024 point output.
What is the correct way of obtaining an FFT on the full 150000 point input?
You could run the FFT on each 1024 point block and average them to get an average power spectrum on the lower-resolution 1024-point frequency axis (512 samples from 0 to the Nyquist frequency, fs/2, so about 10 Hz resolution for your 10 kHz sampling). You should average the magnitudes of the component FFTs (i.e., sqrt(re^2+im^2)), otherwise the average will be sensitive to the drifting phase within each subwindow, which will depend on the precise frequency of the sinusoi.
If you think the periodic component may be at a low frequency, such that it will show up in a 15 sec sample but not complete any cycles in a 1024/10k ~ 100ms sample (i.e., below 10 Hz or so), you could downsample your input. You could try something as crude as averaging every 100 points to get a somewhat-distorted signal at 100 Hz sampling rate, then pack 10.24 sec worth into your 1024 pt sequence to pass to the FFT.
You could combine these two approaches by using a smaller downsampling factor and then do the magnitude-averaging of successive windows.
I'm confused why the system provides an FFT only up to 1024 points - is there something about the memory that makes it harder to access larger blocks?
Calculating a 128k point FFT using a 1k FFT as a subroutine is possible, but you'd end up recoding a lot of the FFT yourself. Maybe you should forget about the system library and use some other FFT implementation, without the length limitation, that will compile on your target. It may not incorporate all the optimizations of the system-provided one, but you're likely to lose a lot of that advantage when you embed it within the custom code needed to use the partial outputs of the multiple shorter FFTs to produce the long FFT.
Probably the quickest way to do the hybrid FFT (1024 points using the library, then added code to combine them into a 128k point FFT) would be to take an existing full FFT routine (a radix-2, decimation-in-time (DIT) routine for instance), but then modify it to use the system library for what would have been the first 10 stages, which amount to calculating 128 individual 1024-point FFTs on different subsets of the original signal (not, unfortunately, successive windows, but the partial-bit-reversed subsets), then let the remaining 7 stages of butterflies operate on those partial outputs. You'd want to get a pretty solid understanding of how the DIT FFT works to implement this.
I use Matlab to calculate the fft result of a time series data. The signal has an unknown fundamental frequency (~80 MHz in this case), together with several high order harmonics (1-20th order). However, due to finite sampling frequency (500 MHz in this case), I always get the mixing frequencies from high order frequency (7-20), e.g. 7th with a peak at abs(2*500-80*7)=440 MHz, 8th with frequency 360 MHz and 13th with a peak at abs(13*80-2*500)=40 MHz. Does anyone know how to get rid of these artificial mixing frequencies? One possible way is to increase the sampling frequency to sufficient large value. However, my data set has fixed number of data and time range. So the sampling frequency is actually determined by the property of the data set. Any solutions to this problem?
(I have image for this problem but I don't have enough reputation to post a image. Sorry for bring inconvenience for understanding this question)
You are hitting on a fundamental property of sampling - when you sample data at a fixed frequency fs, you cannot tell the difference between two signals with the same amplitude but different frequencies, where one has f1=fs/2 - d and the other has f2=f2/2 + d. This effect is frequently used to advantage - for example in mixers - but at other times, it's an inconvenience.
Unless you are looking for this mixing effect (done, for example, at the digital receiver in a modern MRI scanner), you need to apply a "brick wall filter" with a cutoff frequency of fs/2. It is not uncommon to have filters with a roll-off of 24 dB / octave or higher - in other words, they let "everything through" below the cutoff, and "stop everything" above it.
Data acquisition vendors will often supply filtering solutions with their ADC boards for exactly this reason.
Long way to say: "That's how digitization works". But it's true - that is how digitization works.
Typically, one low-pass filters the signal to below half the sample rate before sampling. Otherwise, after sampling, there is usually no way to separate any aliased high frequency noise (your high order harmonics) from the more useful spectrum below (Nyquist) half the sample rate.
If you don't filter the signal before sampling it, the defect is inherent in the sample vector, not the FFT.
FIR filter has to be used for removing the noise.
I don't know the frequencies of the noise that might be adding up into the analog feedback signal I am taking.
My apparatus consists analog feedback signal then i am using ADC to digitize the value now I have to apply FIR filter to remove the noise, Now I am not sure which noise the noise which added up in the analog signal from the environment or some sort of noise comes there due to ADC ?
I have to code this in vhdl.(this part is easy I can do that).
My main problem is in deciding the frequencies.
Thanks in Advance !
I am tagging vhdl as some people who are working in vhdl might know about the filter.
Let me start by stating the obvious: An ADC samples at a fixed rate and can not represent any frequency higher than the Nyquist frequency
Step one: understand aliasing, and that any frequency higher than the Nyquist will alias into your signal as noise. Once you get this you understand that you need an anti aliasing filter in your hardware, in your analog signal path before you digitize it. Depending on the noise requirements of the application you may implement a very complicated 4 pole filter using op-amps; the simplest is to use an RC filter.
Step two: setting the filter cut off. Don't set the cutoff right at the Nyquist frequency, make sure the filter is cutting well before the nyquist (1/2x... 1/10x, depends really how clean and how much noise is present)
So now you're actually kind of over sampling your signal: The filter is cutting above your signal, and the sample rate is high enough such that the Nyquist frequency is sufficiently higher. Over sampling is kind of extra data, that you captured with the intent of filtering further, and possibly even decimating (keeping on in N samples and throwing the rest out)
Step three: use a filter to further remove the noise between the initial cut off of the anti-aliasing filter and the nyquist frequency. This is a science on it's own really, but let me start by suggesting a good decimation filter: Averaging 2 values. It's a box-car filter of order 2, also known as a SINC filter, and can be re applied N times. After N times it is the equivalent of an FIR using the values of the Nth row in pascal's triangle (and divided by their sum).
Again, the filter choice is a science on it's own really. To the extreme is the decimation filters of a sigma-delta ADC. The CS5376A datasheet clearly explains what they're doing; I learn quite a bit just from reading that datasheet!