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11

To be able to analyze what a low pass filter does first you would need to understand what a Fourier transform is, hence some theory first. The Fourier transform essentially represents the time-domain information stored in some function (a square wave in your case) in terms of frequencies. A simple example would be a sine wave $sin(2\pi f_{c} t)$ which ...

9

Make sure that your frequency doesn't reach values below 0 or above the half of your sample rate. Please post more information/code about how you generate your waveform! Chances are you are not doing it correctly. For example, if you want to generate a sine wave with a time-varying frequency $f(t)$ (for example to implement frequency modulation), ...

8

As was pointed out in a comment above, this is a simple consequence of the dynamics of a pendulum. There's nothing particularly signal-processing-related about this problem, just some simple physics and trigonometry. For a pendulum that is displaced from its angular equilibrium point by an angle of $\theta_0$ with an angular velocity of $\omega_0 = 0$ at $t ... 7 I suspect that the accumulator value is growing very large, which causes the float's resolution to degrade. To avoid this you need to occasionally reduce the accumulator to manageable levels. One way to do that is to subtract by 2*pi whenever you exceed 2*pi. 7 The PCM values are proportional to the sound pressure. 8-bit PCM is stored with an offset of 128, so PCM coded values from 0 to 255 code for 'pressure values' from -128 to 127. These values are often normalized to the range -1.0..+1.0. The PCM values are linear representation of the sound pressure, and a log operation is only required if you want to express ... 7 What you see are time-domain samples that correspond to the displacement of a speaker from some rest position as a function of time. For example, the first sample corresponds to the membrane's position at$t=0$, the next represents its position at$t=T$, and so on, assuming that there are$T$seconds between samples. Common sampling intervals for audio ... 7 The "click" is caused by the discontinuity in the waveform and its derivatives - even if the waveform stops at a zero-crossing you might still hear a pop if there's a discontinuity in the higher order derivatives! Its loudness depends on the amplitude at the discontinuity - and it is thus influenced by the length/frequency/phase of the sinusoidal tone. Note ... 7 Interesting project you have going on there! :-) From a signal analysis POV, this is actually a simple question - and yes, you are right that you would utilize the FFT for this frequency estimation problem. I am not familiar with R, but what you essentially want to do is take the FFT of your temperature signal. Since your signal is real, you will get a ... 7 I would recommend doing some proper reading of books/tutorials etc on the Fourier transform and the Discrete Fourier Transform (DFT). You will also want to look at filters and probably convolution for the bandpass filter. But regardless, here's some info that should help with your current state: Use matplotlib to plot the FT that you've calculated: fs = ... 6 The hydrophone has -180 dB 1V/uPa or -60 dB V/Pa. 1 Pa produces hence 1mV or, other way around, the sensitivity is 1mV/Pa. Peak voltage is 5.64 peak to peak. That's 2.82V peak or 2V RMS. A full scale sine wave has 2 V RMS which is 2000 Pa. dBSPL is referenced against 20uPa so 2000 Pa is equivalent to 160 dBSPL. The clipping point of your wave file ... 6 In principle you can, in practice you almost can. The square wave consits of sinusoids with frequencies that are at multiples of the fundamental one (the inverse of the length of one high and one low). These are called harmonics, as you already seem to know. The low pass filter can remove all frequencies above the fundamental one, and you are left with only ... 6 The baseband QAM signal is complex, and the only way to draw it is by doing two drawings, one for the in-phase (real) component, and one for the quadrature (imaginary) component. The passband QAM signal, though, is real, and it is a pulse-shaped carrier whose amplitude and phase depend on each symbol. Myself, I would "draw" it using Matlab or some other ... 4 There is a huge body of research and commercial work on doing acoustic simulation. There are a two basic classes of simulation systems: Finite element or finite boundary: these model the actual physics by dividing air and or/surfaces into small patches and modelling step by step the interaction between the patches by locally solving the wave equations ... 4 For a waveform this smooth and stationary, counting sample points between positive going crossings of some average threshold value will give you a period estimate. Look at several threshold crossing periods to get a more average estimate or detect any trend. 4 I think you posted similar question 3 days ago, regarding your teacher claiming that$\sin 2x$is not a sinusoidal function. Nevertheless this function is definitely sinusoidal. Otherwise how come we can say that signals can be decomposed into sums of sinusoids (and cosinusoids)? You have plenty of orthogonal waves:$\sin x, \ \sin 2x, \ \sin 3x, \ldots$, ... 4 Depends on assumptions you are willing to make and what type of signals are you trying to sample, but in theory I think that sampling rate equal to the Planck time would be a gold standard for anything... This translates to sampling frequency of$1.855 \times 10 ^ {43} \mathtt{Hz}$($18.55$tredecillion hertz). Personally I believe that machines will never ... 4 When using a constant tone audio beacon, beware of room echoes causing multi-path interference and distortion, especially around the leading and trailing portions of your received waveforms. Try using a frequency sweep instead of a constant tone for your transmit waveform. This might provide you with a sharper correlation peak that is less likely to have ... 4 The fundamental property of averaging filters (in swear words, a linear system) is that the output of a sine is a sine of the same frequency, albeit of zero amplitude. So: Which non-trivial moving average weights would you need to find to get a filter that returns the same output as its input? An averaging in phase with the sine: take a filter full of ... 3 If$T_1$remains constant and$T\rightarrow\infty$then you get a single square pulse of length$2T_1$. There won't be another square pulse because the period is infinite.$T_1$constant and$T\rightarrow 0$is indeed nonsensical because the definition of the signal assumes$T_1 < T/2$. If$T$is constant, you can get a constant function if$T_1=T/2$(... 3 Please note that you cannot implement a band-limited oscillator with a pure (stateless) function like: Sample s = saw(x); The reason is that the function must be aware of the rate at which x change to generate a signal with the correct bandwidth For example, let us assume your sample rate is 48kHz. If you call your function in this order: saw(0.00000000);... 3 There is no need to do anything complicated: just measure the duration between peaks of the waveform. This is the period. The frequency is just 1 divided by the period. With about 8 cycles over 2 hours, the frequency is 4 cycles per hour, or about 1 mHz. 3 The x-axis is indeed frequency, but the numbers are quite strange to me. One would expect a scale in powers of 2 (octaves) or of powers of 10 (decades). The y-axis represents the relative magnitude of the signal at that particular frequency. The 0dB level is what you would get from a sine wave with the maximum amplitude (-1..+1). So your P2 is 1.0. 3 http://www.mathworks.com/help/techdoc/ref/wavread.html waveread() has an extra argument that will allow to read data in it's "native" format so you can avoid the output scaling and conversion to double precision. It has also optional output arguments that describe the exact format (sample rate, word width, etc.). The data is supposed to be proportional to ... 3 In the context that you described,$t$is a variable indicating time. That is, the wave will take on a value of$y(t)$at the time instant$t$. If this is measured in seconds, then$\omega$specifies the number of radians that the wave passes through in one second. And, as you noted, if the wave has a frequency of$\frac{100}{15}\ \text{Hz}$, then it will ... 3 I'd like to point out Heisenberg Uncertainty principle, based on which theoretical achievable precision is limited. It states that one can not measure two complementary qualities (e.t. here time and voltage) concurrently and there is a trade off between amount of precision you can get from one or another. In ADCs, for example theoretical limit for ... 3 Is it theoretically possible to perfectly quantize a continuous signal? No. A quantization has an information content obviously countable as bits. Now, if you have a continuously distributed 1D random variable$X$, then the event that any of these real numbers$x$occurred is unbounded ("infinite"): $$I(x) = -\log_2\left(P(X=x)\right)$$ So, for any (non-... 3 No, and the reason is not so much a question of how fast one can sample a continuous-time signal (as the accepted answer and another one says) but rather the impossibility of representing a real number with perfect accuracy via a quantized representation of the real number (as noted in the answer by Marcus Muller). At best, even if we assume an infinite ... 3 Neither of these tones is an exact number of samples at 48 kHz, but you can calculate the periods as follows:$\frac{48000}{441} = 108.84$samples$\frac{48000}{700} = 68.57$samples 3 The AM or medium wave band extends from 526.5 kHz to 1606.5 kHz in Europe or 535 kHz to 1705 kHz in the US. Ultrasound (not supersound! :-) frequencies range from 20kHz and up: However, a bigger problem is that AM stations broadcast using electromagnetic radiation, whereas sound travels by acoustic waves in the air. 3 This is a question where theory and practice will diverge somewhat. Theory I assume that by "frequencies" you mean sinusoids of varying frequency. In that case, yes, you're correct, for any amplitudes$a_1$and$a_2$and frequencies$f_1$and$f_2$(where$f_1 \ne f_2\$), the signals $$x_1(t) = a_1e^{j2\pi f_1 t} \\ x_2(t) = a_2e^{j2\pi f_2 t}$$ are ...

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