I have been looking into how to convert my digital data into analog.
So, I have a two column ASCII data file (x: time, y=voltage amplitude) which I would like to convert into an analog signal (varying Voltage with time). There are Digital to Analog converters, but the good ones are quite expensive. There should be a more trivial way to achieve this.
Ultimately what I'd like to do is to reconstruct the original time variant voltage which was sampled every nano-second and recorded as an ASCII data file.
I thought I may feed the data into my laptop's sound card and re-generate the time variant voltage which I can then feed into the analyzer via the audio jack. Does this sound feasible?
I am not looking into recovering the "shape" but the signal (voltage) itself.
Puzzled on several accounts.
You want to convert into an analog signal (varying Voltage with time) But the what you already have, the discrete signal, is indeed a "varying voltage with time", only that both the values (voltages) and times are discrete. That's the way computers (digital equipment, in general) work.
Only when the signal goes to some non-discrete medium (eg. a classical audio cable+plug) we have an analog signal. Precisely, the sound card of your computer is at its core a "Digital to Analog converter".
So, it appears you are not trying to do some digital processing of your signal (interpolation, or whatever), you are not dealing with computer programming, but with a hardware thing: getting the signal to a cable. If so, SO is not the proper place. YOu might try https://electronics.stackexchange.com/ ...
But, on another thing, you say that your data was "sampled every nano-second". That means 1 billion samples per second, or a sample freq of 1Ghz. That's a ridiculously high frequency, at least in the audio world. You cant output that to a sound card, which would be limited to the audio range (about 48Khz = 48000 samples per second).
You want to just fit a curve to the data. Assuming the sampling rate is sufficient, a third-order polynomial would be plenty. At each point N, you fit a cubic polynomial to points N-1, N, N+1, and N+2, and then you have an analytic expression for the data values between those points. Shift over one, and repeat. You can average the values for multiple successive curves, if you want.
Related
I am building a dB meter as part of an app I am creating, I have got it receiving the peak and average power's from the mic on my iPhone (values ranging from -60 to 0.4) and now I need to figure out how to convert these power levels into db levels like the ones in this chart http://www.gcaudio.com/resources/howtos/loudness.html
Does anyone have any idea how I could do this? I can't figure an algorithm out for the life of me and it is kind of crucial as the whole point of the app is to do with real word audio levels, if that makes sense.
Any help will be greatly appreciated.
Apple's done a pretty good job at making the frequency response of the microphone flat and consistent between devices, so the only thing you'll need to determine is a calibration point. For this you will require a reference audio source and calibrated Sound Pressure level meter.
It's worth noting that sound pressure measurements are often measured against the A-weighting scale. This is frequency weighted for the human aural system. In order to measure this, you will need to apply the relevant filter curve to results taken form the microphone.
Also be aware of the difference between peak and mean (in this case RMS) measurements.
As far as I can tell from looking at the documentation, the "power level" returned from an AVAudioRecorder (assuming that's what you're using – you didn't specify) is already in decibels. See here from the documentation for averagePowerForChannel:
Return Value
The current average power, in decibels, for the sound
being recorded. A return value of 0 dB indicates full scale, or
maximum power; a return value of -160 dB indicates minimum power (that
is, near silence).
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
How can I get the frequency for an audio input on iPhone? Is it necessary to use a FFT if I'm only interested in finding a specific frequency (i.e. within a timeframe of x milliseconds, check if there is a peak at y Hz)?
If you're just interested in a specific, fixed frequency (i.e. a pure tone) then you can use the Goertzel algorithm which is very simple to implement and relatively lightweight (computationally) compared to an FFT.
Using GNU octave, I'm computing a fft over a piece of signal, then eliminating some frequencies, and finally reconstructing the signal. This give me a nice approximation of the signal ; but it doesn't give me a way to extrapolate the data.
Suppose basically that I have plotted three periods and a half of
f: x -> sin(x) + 0.5*sin(3*x) + 1.2*sin(5*x)
and then added a piece of low amplitude, zero-centered random noise. With fft/ifft, I can easily remove most of the noise ; but then how do I extrapolate 3 more periods of my signal data? (other of course that duplicating the signal).
The math way is easy : you have a decomposition of your function as an infinite sum of sines/cosines, and you just need to extract a partial sum and apply it anywhere. But I don't quite get the programmatic way...
Thanks!
The Discrete Fourier Transform relies on the assumption that your time domain data is periodic, so you can just repeat your time domain data ad nauseam - no explicit extrapolation is necessary. Of course this may not give you what you expect if your individual component periods are not exact sub-multiples of the DFT input window duration. This is one reason why we typically apply window functions such as the Hanning Window prior to the transform.