I wonder if there is any use of phase spectrum, or we use amplitude information for all the tasks avaliable?
Yes. You can't reconstruct or filter a signal without the phase spectrum in addition to the amplitude information.
Related
I am implementing a Deep Q-Learning algorithm. One thing I'm not fully getting my head around is the step where you take your batch sample from the experience queue and use that to calc the q values for the next states. This includes a secondary question about the input shape of the cnn that I'm training the policy to. My question is conceptual; do I pass the entire sampled batch into the model all at once or 1 at a time, then calculate the loss? If the entire batch that implies my CNN needs that batch size at the input layer and that when I implement the policy, I'll need to collect that number of batches before calling the inference function.
Thanks for any insight.
Question regarding sampling -
The purpose of sampling from the replay buffer is to train your deep neural network. DQN is an off-policy algorithm. Therefore, even though you are following an epsilon greedy policy (usually), your agent can learn a better policy from the minibatch of sampled experiences. We randomly sample the replay buffer so that your data follows the i.i.d assumption.
Question regarding batch size -
Most DL frameworks are set up so that your network can take in a varying batch size as input or have a simple workaround for it.
I'm currently attempting to send and receive some BPSK modulated data through sound. Currently, I'm using goertzel's algorithm as a bandpass filter for demodulation. I have no formal training in signal processing.
Given a sample rate of 44100Hz and a bucket size of 100, my intuition says that generating a wave at a frequency multiple of 441hz should result in me picking up a relatively constant phase. At other frequencies, the phase i detect should drift.
However, my current implementation shows a drift in phase when detecting a generated sound wave over the course of a second (around 90 degrees). Is this to be expected or a sign of a flaw in my implementation of goertzels?
Furthermore, is there a better, perhaps obvious way to detect the phase of a wave at a specific frequency then using goertzels?
A slow phase drift can be the result of a small difference in the clock frequencies of the transmitter and receiver. This is to be expected.
Usually BPSK data is differentially encoded so you only need to detect the moments when the phase shifts by 180 degrees, and any slow phase drift or offset can be easily ignored.
You will need to perform some form of carrier recovery and symbol recovery to track and correct offsets in transmitter and receiver clocks
im have RSSI readings but no idea how to find measurement and process noise. What is the way to find those values?
Not at all. RSSI stands for "Received Signal Strength Indicator" and says absolutely nothing about the signal-to-noise ratio related to your Kalman filter. RSSI is not a "well-defined" things; it can mean a million things:
Defining the "strength" of a signal is a tricky thing. Imagine you're sitting in a car with an FM radio. What does the RSSI bars on that radio's display mean? Maybe:
The amount of Energy passing through the antenna port (including noise, because at this point no one knows what noise and signal are)?
The amount of Energy passing through the selected bandpass for the whole ultra shortwave band (78-108 MHz, depending on region) (incl. noise)?
Energy coming out of the preamplifier (incl. Noise and noise generated by the amplifier)?
Energy passing through the IF filter, which selects your individual station (is that already the signal strength as you want to define it?)?
RMS of the voltage observed by the ADC (the ADC probably samples much higher than your channel bandwidth) (is that the signal strength as you want to define it?)?
RMS of the digital values after a digital channel selection filter (i.t.t.s.s.a.y.w.t.d.i?)?
RMS of the digital values after FM demodulation (i.t.t.s.s.a.y.w.t.d.i?)?
RMS of the digital values after FM demodulation and audio frequency filtering for a mono mix (i.t.t.s.s.a.y.w.t.d.i?)?
RMS of digital values in a stereo audio signal (i.t.t.s.s.a.y.w.t.d.i?) ?
...
as you can imagine, for systems like FM radios, this is still relatively easy. For things like mobile phones, multichannel GPS receivers, WiFi cards, digital beamforming radars etc., RSSI really can mean everything or nothing at all.
You will have to mathematically define away to describe what your noise is. And then you will need to find the formula that describes your exact implementation of what "RSSI" is, and then you can deduct whether knowing RSSI says anything about process noise.
A Kalman Filter is a mathematical construct for computing the expected state of a system that is changing over time, given an initial state and noisy measurements of that system. The key to the "process noise" component of this is the fact that the system is changing. The way that the system changes is the process.
Your state might change due to manual control or due to the nature of the system. For example, if you have a car on a hill, it can roll down the hill naturally (described by the state transition matrix), or you might drive it down the hill manually (described by the control input matrix). Any noise that might affect these inputs - wind, bumps, twitches - can be described with the process noise.
You can measure the process noise the way you would measure variance in any system - take the expected dynamics and compare them with the true dynamics to generate a covariance matrix.
I am developing a back-end speech recognition software wherein the user can import mp3 files. How can I extract the features from this digital audio file? should I convert it back to analog first?
Your question is unclear, since you are using terms analog and digital incorrectly. Analog is a real-world, continuous function, i.e. voltage, pressure, etc. Digital is a discrete (sampled) and quantized version of the analog signal. You must calculate the FFT of your audio frames when calculating the MFCC's. You can extract MFCC's only from the digital signal - it's rather impossible to do it with the analog one.
If you are asking about whether it is possible to extract the MFCC's from an mp3 file, then yes - it is possible. All you need is to perform the standard algorithm and you can get your features - obviously it is outside of spec of that question.
Calculate the FFT for frames of data.
Calculate the PSD by squaring the samples.
Apply the mel-filterbank and sum the energy across banks.
Calculate the logarithm of each of the energies.
Calculate the DCT of the logarithms of energies.
You're confusing things here, like #jojek said you can do all that WITH the digital signal. This here is a pretty spot on tutorial:
http://practicalcryptography.com/miscellaneous/machine-learning/guide-mel-frequency-cepstral-coefficients-mfccs/
This one is more practical:
http://www.speech.cs.cmu.edu/15-492/slides/03_mfcc.pdf
From Wikipedia: [http://en.wikipedia.org/wiki/Mel-frequency_cepstrum]
MFCCs are commonly derived as follows:[1][2]
Take the Fourier transform of (a windowed excerpt of) a signal. Means short time fourier transform)
Map the powers of the spectrum obtained above onto the mel scale, using triangular overlapping windows. (Calculation described in the links above)
Take the logs of the powers at each of the mel frequencies.
Take the discrete cosine transform of the list of mel log powers, as if it were a signal.
The MFCCs are the amplitudes of the resulting spectrum.
and here's a Matlab toolbox to help you understand it better:
http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html
I'm working on this embedded project where I have to resonate the transducer by calculating the phase difference between its Voltage and Current waveform and making it zero by changing its frequency. Where I(current) & V(Voltage) are the same frequency signals at any instant but not the fixed frequency signals approx.(47Khz - 52kHz). All I have to do is to calculate phase difference between these two signals. Which method will be most effective.
FFT of Two signals and then phase difference between the specific components
Or cross-correlation of two signals?
Or another if any ? Which method will give me most accurate result ? and with what resolution? Does sampling rate affects phase difference's resolution (minimum phase difference which can be sensed) ?
I'm new to Digital signal processing, in case of any mistake, correct me.
ADDITIONAL DETAILS:-
Noise In my system can be white/Gaussian Noise(Not significant) & Harmonics of Fundamental (Which might be significant one in resonant mismatch case).
Yes 4046 can be a good alternative with switching regulators. I'm working with (NCO/DDS) where I can scale/ reshape sinusoidal on ongoing basis.
Implementation of Analog filter will be very complex as I will require higher order filter with high roll-off rate for harmonic removal , so I'm choosing DSP based filter and its easy to work with MATLAB DSP Processors.
What sampling rate would you suggest for a ~50 KHz (47Khz-52KHz) system for achieving result in FFT or Goertzel with phase resolution of preferably =<0.1 degrees or less and frequency steps will vary from as small as ~1 to 2Hz . to 50 Hz-200Hz.
My frequency is variable 45KHz - 55Khz ... But will be known to my system... Knowing phase error for the last fed frequency is more desirable. After FFT AND DIGITAL FILTERING , IFFT can be performed for more noise free samples which can be used for further processing. So i guess FFT do both the tasks ...
But I'm wondering about the Phase difference accuracy cause thats the crucial part.
The Goertzel algorithm http://www.embedded.com/design/configurable-systems/4024443/The-Goertzel-Algorithm is a fairly efficient tone detection method that resolves the signal into real and imaginary components. I'll assume you can do the numeric to get the phase difference or just polarity, as you require.
Resolution versus time constant is a design tradeoff which this article highlights issues. http://www.mstarlabs.com/dsp/goertzel/goertzel.html
Additional
"What accuracy can be obtained?"
It depends...upon what you are faced with (i.e., signal levels, external noise, etc.), what hardware you have (i.e., adc, processor, etc.), and how you implement your solution (sample rate, numerical precision, etc.). Without the complete picture, I'll be guessing what you could achieve as the Goertzel approach is far from easy.
But I imagine for a high school project with good signal levels and low noise, an easier method of using the phase comparator (2 as it locks at zero degrees) of a 4046 PLL www.nxp.com/documents/data_sheet/HEF4046B.pdf will likely get you down to a few degrees.
One other issue if you have a high Q transducer is generating a high-resolution frequency. There is a method but that's another avenue.
Yet more
"Harmonics of Fundamental (Which might be significant)"... hmm hence the digital filtering;
but if the sampling rate is too low then there might be a problem with aliasing. Also, mismatched anti-aliasing filters are likely to take your whole error budget. A rule of thumb of ten times sampling frequency seems a bit low, and it being higher it will make the filter design easier.
Spatial windowing addresses off-frequency issues along with higher roll-off and attenuation and is described in this article. Sliding Spectrum Analysis by Eric Jacobsen and Richard Lyons in Streamlining Digital Signal Processing http://www.amazon.com/Streamlining-Digital-Signal-Processing-Guidebook/dp/1118278380
In my previous project after detecting either carrier, I then was interested in the timing of the frequency changes in immense noise. With carrier phase generation inconstancies, the phase error was never quiescent to be quantified, so I can't guess better than you what you might get with your project conditions.
Not to detract from chip's answer (I upvoted it!) but some other options are:
Cross correlation. Off the top of my head, I am not sure what the performance difference between that and the Goertzel algorithm will be, but both should be doable on an embedded system.
Ad-hoc methods. For example, I would try something like this: bandpass the signals to eliminate noise, find the peaks and measure the time difference between the peaks. This will probably be more efficient, and, provided you do a reasonable job throwing out outliers and handling wrap-around, should be extremely robust. The bandpass filters will, themselves, alter the phase, so you'll have to make sure you apply exactly the same filter to both signals.
If the input signal-to-noise ratios are not too bad, a computually efficient solution can be built based on zero crossing detection. Also, have a look at http://www.metrology.pg.gda.pl/full/2005/M&MS_2005_427.pdf for a nice comparison of phase difference detection algorithms, including zero-crossing ones.
Computing 1-bin of a DFT (or using the similar complex Goertzel block filter) will work if the signal frequency is accurately known. (Set the DFT bin or the Goertzel to exactly that frequency).
If the frequency isn't exactly known, you could try using an FFT with an FFTshift to interpolate the frequency magnitude peak, and then interpolate the phase at that frequency for each of the two signals. An FFT will also allow you to window the data, which may improve phase estimation accuracy if the frequency isn't exactly bin centered (or exactly the Goertzel filter frequency). Different windows may improve the phase estimation accuracy for frequencies "between bins". A Blackman-Nutall window will be better than a rectangular window, but there may be better window choices.
The phase measurement accuracy will depend on the S/N ratio, the length of time one samples the two (assumed stationary) signals, and possibly the window used.
If you have a Phase Locked Loop (PLL) that tracks each input, then you can subtract the phase coefficients (of the generator components) to determine offset between the phases. This would also be robust against noise.