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I am working with a dataset that contains a binary signal similar to the one depicted in the plot below. The goal is to develop a data cleaning function to eliminate incomplete square patterns within the signals, as exemplified by the shaded box. (Note that the illustration serves primarily for visual clarity; the original signals exhibit irregularities in terms of the duration of each square and the time gaps between them.) The invalid cycles in the dataset are essentially due to missing points. Therefore, the invalid cycles will be the ones that deviate significantly from the square shape.
One challenge in this data processing task is the dataset's sheer size, which may have tens of millions of rows. Thus, I have been researching signal processing libraries and vectorized approaches to circumvent the need for iterative loops. One approach I have explored involves calculating the gradient of the signal using NumPy to identify the start and end points of valid signals, those that form perfect square shapes. However, I am encountering difficulties in using this information to filter out the rows corresponding to the invalid signals from my dataframe. Another possibility might be using some sort of convolution, but I do not have much experience in this type of analysis.
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We present a rapid and accurate method of calibrating seismic systems using a random binary calibration signal and cross-spectral techniques. The complex transfer function obtained from the cross spectrum is least-squares fit to the ratio of two polynomials in s(s = iω) whose degrees are determined by a linear systems analysis. This provides a compact representation of the system frequency response. We demonstrate its application to two seismic systems, the IDA and SRO seismomenters. This method yields calibrations to an accuracy of better than 1 per cent in amplitude and 1 in phase.
Signals of interest. Different types of binary temporal patterns that need to be extracted from the time course microarray data. (a) Gene expressions transition from a low value to a high value. (b) Gene expressions transition from a high value to a low value. (c) Gene expressions transition from low to high and return to the same low value. (d) gene expressions transition from high to low and return to the same high value.
Figure 3A describes the proportion of correctly identified gene expression patterns as a function of different step heights, where the position of the steps are fixed at certain time points. All single steps are fixed at the fifth position and all binary two steps are fixed at the fifth and nineth positions. As can be seen in the figure, when the step height is 5σ, StepMiner identifies genes correctly over 90% of the time. As the step height is reduced relative to the noise level, the proportion of correct identifications drops dramatically (as expected). The drop in accuracy is higher for two-step signals because of the greater degrees of freedom for those signals.
Figure 3C shows the sensitivity of StepMiner to the number of time points and the P-value threshold. As can be seen from the figure, accurate matching of two-step signals requires more time points than matching of one-step signals. The proportion of matches can be increased by increasing the P-value threshold, but only at the cost of an increased FDR (which can be measured and adjusted as described in False Discovery Rate section).
For comparison, it is possible to reanalyze the data using gene sets derived from StepMiner. Binary signals were extracted from the diauxic shift data, using a P-value cutoff of 0.05, resulting in an FDR of 15%. Out of a total of 2284 genes in the diauxic shift data, 1088 were matched to single steps, 267 were matched to binary two steps and 929 did not match anything. The fitting step functions are shown for three genes in Figure 4. A heat map of the genes expression profiles appears in Figure 4. In the heat map, the top genes are those that change once, the rising genes first, and falling genes second. Lower, there is a group of genes that go up then down, and last, the genes that go down then up. Each of these groups is sorted by the time of first change. The ordered response of genes to stimuli is immediately evident when so depicted. The heat map also makes apparent two discontinuities, at 8.25 h and 9.25 h. These correspond to observed changes in the growth rate of the yeast around 9 h.
Even when the gene expression level over time is only approximately binary, we find that the results produced by StepMiner are sensible. For example, consider the measurements for the genes in Figure 4. In each case, the behavior of the gene may be complex or noisy, but StepMiner reports reasonable (and objective) results about when each gene becomes up-regulated.
Replicated measurements at the same time point should not be averaged. Instead, they should be handled using the same matching algorithm as sequential measurements, except that the algorithm should not try to put a step between simultaneous measurements. With this processing, they can directly improve the P-values of extracted signals.
But according to the defintion, the signal should be discrete in time to be a digital signal. In the plot, a binary signal is drawn as continuous in time. Then how can this be a digital signal according to the defintion.
Also I read that a digital signal has different meaning/definition in different contexts.For example the above mention definition is apt in the signal processing context, whereas in digital electronics where the binary signal mention above is used, a digital signal is a signal that takes only discrete amplitude values(ie. it is quantized in amplitude) and it can be continuous or discrete in time.
A physical signal between two or more points, such as in RS232, PCI express and many others that happen to take on a discrete number of states (in this case 2), is continuous in time, as are all physical layer signals.
But according to the definition, the signal should be discrete in time to be a digital signal. In the plot, a binary signal is drawn as continuous in time. Then how can this be a digital signal according to the definition.
The horizontal line tells you that the value is unchanging for that period of time. Your first, binary timing diagram might be the output of a serial connection. It's low for one clock cycle then high for one clock cycle, etc. It's what you would see if you monitored the signal on an oscilloscope.
If you have a signal in Seeq that is an integer representing an 8-bit 16-bit or 32-bit set of states here is some example code you can use to convert the integer signal into 8-16-32 separate 0/1 signals that can be used to define machine states elsewhere in the Seeq platform
However, for those electronic circuits that implement binary logic operators using physical devices (gates etc.), the associated voltage and current waveforms are analog in nature. What's binary there is the information that the voltage or current waveform carries. But the physical existance is analog. So if you want to plot them, then you would do it just like a logic analyser (oscilloscope) would draw them on their phosphorus crt screen...
How do i convert an audio signal to binary without using bitsplit from creb external in Pure Data ?. Do i need to use snapshot in combination with something else or there is a better way ? I was thinking about doing signal quantification using snapshot and then converting the decimal magnitude to binary. Is this the right way or is something else that i miss ? Many thanks.
what do you mean? Audio is already in binary floating-point.. do you want to print every binary place-value of every single sample somewhere? Or could it be every 64 samples? (in which case I would go the snapshot route)
@seb-harmonik.ar Yes i need somehow to extract all the binary digits from an audio signal for every single sample. The idea is to then apply bitwise synthesis to the binary signal and converting back to audio. So i can have a XOR gate performing bitwise operation on 2 binary vectors from 2 audio sources.
@Boran Robert I copy this from another thread as a thought: "...plus in general, it's just never a real good idea to try to do audio signal processing with control signals (except for stuff like LFO's PWMS or other 'slow' modulations perhaps)..."
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@Boran-Robert I try using snapshot but it is not ok. It is not stable and it gives me negative numbers. Negative numbers from decimal to binary requires additional conversion to 2's complement which i don't want. Sign magnitude is not good because i will have -0 and 0 for representing the same zero.
@alexandros Thank you very much. I need to further test this ideas. So more precisely i want to make bitwise XOR modulation on two sine waves. The problem is i don't now what i am missing. Another problem with "&" and "" operations are that i need them as inputs to be already in binary form. So this operations "&" and "" don't work with [expr] only [expr]. But yes i would like to use [expr] because converting the signals to binary form and then back to signal is not easy. Also for the carry oscillator i was thinking to use unipolar signal instead of bipolar.
I think we should clarify further what your intentions are.. Are you keeping the audio signals as floating point numbers in the range of 0 to 1 or 0 to 2? Do you want to XOR the floating point numbers or only their "integer" parts? If you XOR the raw binary representation of 2 floating point numbers I feel like the results would be way more unpredictable than in fixed point/integer because of XOR ing the exponents.. it makes my head hurt just to think about the results of that and I doubt you could do it in pd vanilla anyhow..
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