# Questions tagged [moving-average]

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### Impulse Response of a Moving Average System

According to Discrete Time Signal Processing by Al Oppenheim 3rd Edition, the impulse response of a moving average filter is as below My question is that shouldn't h[n] be having the dirac delta ...
38 views

### Magnitude and phase response and cut-off frequency of a moving average filter

The frequency response of a typical moving average filter of length $N$ is given by $H(\omega)=\frac{1}{N}\frac{\sin(\omega N/2) e^{-j \omega ((N-1)/2)}}{\sin(\omega/2)}$. Firstly, isn't the cut off ...
36 views

### temporal smoothing: FWHM of Gaussian kernel vs. window length of moving average

Suppose in one case I convolve Gaussian kernel with FWHM=10 samples. I would like to compare the result with moving average. My question: should I take the moving average window also 10 samples? In ...
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### Is it correct to call a Savitsky-Golay filter of degree 0 a simple moving average?

I had this question after seeing that polynomial regressions fit polynomial functions of different degrees to a time-series, since the mean of a time series is a constant and that a constant is also a ...
146 views

I want to implement in fixed point arithmetic an exponential moving average filter, with a specific cutoff frequency for a given sampling rate. The formula for the filter is $$y_n = \alpha x_n + (1 -... 0answers 7 views ### After fitting auto ARIMA's order, in prediction I'm getting bad result For sunspot dataset. Below is the ARIMA code. Auto ARIMA finds the best ARMA(2,1,2)(2,0,1) model. But when I plot the prediction seems wrong: ... 1answer 33 views ### Differences in moving window rms due to sampling rate I have a 10 second recorded signal band pass filtered from 100-500 Hz. The original sampling rate is 10 kS. Now I run a moving window RMS with a window length: 10 ms on the signal (10/1000 * sampling ... 2answers 58 views ### How to discard deviating values from standard deviation and running average I'm building a inductive vehicle loop detector. By measuring the frequency of a LC-oscillator where the cars will pass over the inductor of the LC-Oscillator. If the cars pass over the inductor the ... 1answer 405 views ### Moving average filter for sound in MATLAB [closed] y[n] = b0x[n] +b1x[n-1] I have this MA filter in matlab as following ... 1answer 142 views ### Calculating filter coefficients of a Moving average with error correction I have an oversampling ADC where I need to correct Gain/offset errors 'during' each conversion. This also links to my previous question - Moving average and linearization of two piecewise linear ... 0answers 53 views ### Moving average and linearization of two piecewise linear systems I have 2 oversampling ADC's running parallelly, each to process data in a specific range of the input as shown below: Each ADC can process only half cycle range of a sine wave. Each ADC adds its own ... 1answer 267 views ### Is there a clever way to implement cascaded moving average filters? I'd like to effeciently approximate a gaussian filter's step response using cascaded moving average filters. I know about recursive moving average, but is there some clever algorithm to cascade them ... 2answers 61 views ### How do you properly organize data to compute multiple (independent) recursive filters at the same time taking advantage of SIMD instructions? I'm processing multiple (independent) Exponential Moving Average 1-Pole filters on different parameters I have within my Audio application, with the intent of smooth each param value at audio rate: <... 1answer 77 views ### ARMA & MA methods: how do you know the error terms? Reading the ARMA model for the first time, and I'm confused. Let's say I have a time series x = [1, 2.1, 2.9, 3, 4.1] According to the ARMA model, X_t is a ... 2answers 851 views ### Moving Average for Notch filtering I have a periodic signal(ECG) with period of ~1 seconds. It does not have features that are shorter than 0.04 seconds. For removal of 60Hz, I thought instead of implementing a notch filter, doing a ... 1answer 112 views ### Moving average algorithm that conserves integral Suppose I have point array y_i of size N. How to implement moving average algorithm that conserves quantity$$ I = \sum_{i=1}^{N}y_i $$NOTE: I don't want time shift so I would prefer to use ... 1answer 88 views ### A general conceptual understanding of moving average I have a conceptual question here. I understood how to calculate a Moving Average(MA). For example : x(n) = 0, 1, 2, 3, 4, 5 MA = 0, 1/2, 3/2, 5/2,7/2, 9/2, where for calculation of the MA we only ... 6answers 381 views ### Optimal  n  -th Order IIR /AR Approximation of a Moving Average Filter I would like to approximate a moving average filter with an IIR filter of much lower order than the tap-length of the moving average filter. Optimality shall refer to the L_2 norm of the impulse ... 2answers 377 views ### Mean delay for a M tap harmonically weighted filter I am trying to derive the mean delay for M filter taps harmonically weighted:$$y[n] = \frac{M\,x[n] + (M-1)x[n−1]... + 1 \cdot x[n−M+1]}{\tfrac12 M (M + 1)}$$. For a uniformly weighted filter, I ... 3answers 602 views ### Denoising a signal I'm starting hydraulic experiments, where I'd have to measure velocity in an unsteady flow with a device called Acoustic Doppler Velocimeter. In DSP terms, I'd have a nonstationary signal in a shape ... 1answer 173 views ### Sampling multiple sensors at different rates I have a question regarding how best to sample data from multiple sensors when they are all updating at different/changing rates. I am new to data acquisition so please bear with me. For my Master's ... 2answers 178 views ### How to make the impulse response sparse? How does one know that the channel is sparse? I am new to sparse channel estimation algorithms and reading research articles. One such paper is blind sparse channel estimation using a modification of the BOMP technique titled, "Blind Acoustic ... 1answer 123 views ### Should I use window or any filtering to average my data? I have 80 seconds of data and I have to score my data by taking the average or median (or some other method) every 10 seconds. What's the best way to do this ? Should I just use a regular rectangular ... 2answers 44 views ### Confusion regarding model order and lags I have similar questions as the one asked in these posts: https://stackoverflow.com/questions/47083890/fir-filter-length-is-the-intercept-included-as-a-coefficient-matlab/47085339?noredirect=1#... 1answer 127 views ### Underdetermined deconvolution of windowed output Consider a discrete 'blurred' output h[t] given by the convolution of filter f[t] and signal g[t]. This question considers recovering g[t] from a window (subset) of h[t]. This causes the ... 1answer 223 views ### Model validation after estimation — system identification — help with an example in Matlab QUESTION: I want to determine how well the estimated model fits to the future new data. How do I validate the estimated model...what is the procedure? After system identification, how to do model ... 1answer 2k views ### Lowpass : What is wrong with average filtering? The question is : What is wrong with averaging as low pass filter ? The details : I want to lowpass filter a signal to downsample it. The constraints are : I have no RAM available and I work in ... 1answer 142 views ### Why dft of moving average impulse response has 0 angle I wanted to visualise angle and magnitude of moving average DFT. I used python3 for that: ... 3answers 2k views ### Group delay of moving average filter I have implemented a moving average filter (in Python) where I fill a list with values and average them. When new values arrive the oldest will be deleted. Now I am wondering how much delay I get ... 0answers 36 views ### Multitapering in time domain to obtain smoother filtered signals? Suppose we want to approximate the instantaneous power z(n) = |y(n)|^2 of the discrete-time signal y(n), where y(n) is the result of filtering x(n) with a given window h(n), y(n) = x(n) \... 1answer 345 views ### autoregressive moving average code implementation I am new to DSP and i am trying to take a wav (human speech) file and apply ARMA filter and plot its PSD graph in python. I see that there are a lot of AR implementations but almost none ARMA. I ... 5answers 3k views ### What is the transfer function of a moving average? To make post-processing easier, I export scope measurements as CSV files, which are then post-processed (mostly in Microsoft Excel, which is not the best tool for the job, but it is all I have at my ... 1answer 129 views ### Terminologies - lags, order in time series model I am facing some difficulties with the terminologies - lag (p) and sequence length (number of data points) (N) used in time series model such as Moving average and Autoregressive model. Considering ... 2answers 125 views ### MATLAB: Implementing Least Squares Estimator for a Given Model The formula to estimate \mathbf{h} is then$$\hat{\mathbf{h}} = (X^T X)^{-1} X^T \vec{y}\tag{2}$$I think this can be implemented in Matlab using ... 1answer 142 views ### How to Apply Least Squares Estimation for Sparse Coefficient Estimation? The model is expressed as,$$y(n) = \sum_{i=0}^{p-1} r(i) x(n-i) + v(n) \tag{1}$$where \mathbf{r} = [r_1,r_2,\ldots,r_p]^T is the sparse channel coefficients of length p, \mathbf{x} = [x_1,x_2,.... 2answers 368 views ### MAD and RMS SNR relation Recently I've found a formula relating mean average deviation (MAD) SNR to root mean square (RMS) SNR:$$\text{SNR}_\text{MAD} = \sqrt{\frac{2}{\pi}} \text{SNR}_\text{RMS} $$which assumes Gaussian ... 1answer 395 views ### Determination of periodicity in data and finding mean I have to find whether there is any pattern (I mean periodicity or close to periodicity) and if there is, for one cycle i have to perform numerical integration to determine mean. In the first picture ... 1answer 558 views ### How to approximate the sample rate? I have a simple program that captures audio from an audio device. I have configured a nominal sample rate of 48000Hz and a buffer size of 1 millisecond. The audio sub system should execute my capture ... 1answer 314 views ### N point moving average filters in state space I am new to this filter, I did read about them, but could find out a state space notation of these:$$y(n)=\frac{1}{N}\sum_{m=0}^{N-1}x(n-m)$$Are moving average filters an LTI systems? And how do ... 1answer 2k views ### Difference between Gaussian and moving average filters for peak detection and doppler shift detection? Consider having a signal in the time domain, and you want to smooth the signal. Moving average and Gaussian filters that are used. How do you choose which is used for what? What are the conditions ... 1answer 1k views ### How does this “simple filter” work? I'm new to DSP, and I'm using this basic "1-pole LPF" Param Smooth filter which "smooth" param when I change it. The code is pretty simple: ... 1answer 70 views ### Help in problem formulation for estimation of image as a feature vector - SISO or MIMO FIR channel model? Based on the paper Blind Image deconvolution: A feature vector is a list of numbers used to represent an image. The feature vector for my case takes values as symbols -1,1. An instance or an ... 2answers 1k views ### Moving Average of sinusoid If you calculate a simple moving average over a window length that is equal to the period of the sinusoid, you get a straight line (=0 because the wave is symmetric around the X-axis): the wave has a ... 1answer 72 views ### Envelop detection with low sample rate? I have a signal up to 3\textrm{ MHz}. The ADC that sample it has a rate of 1.5\mu s. So a full T of the signal is 0.3\mu s, and I can only sample each 1.5\mu s. It sounds not enough, but I ... 3answers 2k views ### Determine whether a signal is increasing or decreasing over time I have a signal (x-axis: Time, y-axis: Data) which has more than 10000 samples per second. The signal itself represents some physical data (e.g. speed, acceleration, etc.) and has some noise on it. ... 1answer 148 views ### Generalized/Power means in DSP Generalized/power means may be used to construct moving-average filters with different properties than regular one which is based on arithmetic mean. This observation seems to be trivial - even ... 1answer 1k views ### How to select the length of a smoothing moving average filter? I have a time series signal I need to smoothen to get rid of some noise. I decided to apply a moving average filter to this signal. I know the choice of the length of the MA is critical. How should ... 2answers 98 views ### How is that after random numbers with their negatives alternating passing through 5, 4, 3 order moving average filter, become quasi sinusoidals? I have passed random numbers$${89, 58, 13, 70, 24} with their negatives alternating, through 5 order moving average filter and output was positive and negative numbers alternating. After I have ...
In order to know if my signal is increasing or decreasing, I'm using the discrete derivative $y[n] = x[n] - x[n-1]$ or a smoothed version of it (for example Exponential Weight Moving Average of $y[n]$ ...