Perform and interpret basic frequency-domain signal analysis. The example discusses the advantages of using frequency-domain versus time-domain representations of a signal and
Create a signal consisting of three noisy sinusoids and a chirp, sampled at 200 kHz for 0.1 second. The frequencies of the sinusoids are 1 kHz, 10 kHz, and 20 kHz. The sinusoids have different
Resolve closely spaced sine waves using subspace methods. Subspace methods assume a harmonic model consisting of a sum of sine waves, possibly complex, in additive noise. In a
In general terms, one way of estimating the PSD of a process is to simply find the discrete-time Fourier transform of the samples of the process (usually done on a grid with an FFT) and
Use the discrete Fourier transform to construct a linear regression model for a time series. The time series used in this example is the monthly number of accidental deaths in the United
Obtain nonparametric power spectral density (PSD) estimates equivalent to the periodogram using fft . The examples show you how to properly scale the output of fft for even-length inputs,
Reduce bias and variability in the periodogram. Using a window can reduce the bias in the periodogram, and using windows with averaging can reduce variability.
The modified periodogram windows the time-domain signal prior to computing the DFT in order to smooth the edges of the signal. This has the effect of reducing the height of the sidelobes or
An improved estimator of the PSD is the one proposed by Welch. The method consists of dividing the time series data into (possibly overlapping) segments, computing a modified periodogram of
The following sections discuss the performance of the periodogram with regard to the issues of leakage, resolution, bias, and variance.
One application of Welch's method is nonparametric system identification. Assume that H is a linear, time invariant system, and x ( n ) and y ( n ) are the input to and output of H , respectively.
Use the cross spectrum to obtain the phase lag between sinusoidal components in a bivariate time series. The example also uses the magnitude-squared coherence to identify significant
Measure the power of deterministic periodic signals. Although continuous in time, periodic deterministic signals produce discrete power spectra.
Use zero padding to obtain an accurate estimate of the amplitude of a sinusoidal signal. Frequencies in the discrete Fourier transform (DFT) are spaced at intervals of F_s/N , where F_s is the
Generate 1024 samples of a chirp sampled at 1024 kHz. The chirp has an initial frequency of 50 kHz and reaches 100 kHz at the end of the sampling. Add white Gaussian noise such that the
Perform and interpret basic time-frequency signal analysis. In practical applications, many signals are nonstationary. This means that their frequency-domain representation (their
The periodogram can be interpreted as filtering a length L signal, x_L(n) , through a filter bank (a set of filters in parallel) of L FIR bandpass filters. The 3 dB bandwidth of each of these
Perform spectral analysis on nonuniformly sampled signals. It helps you determine if a signal is uniformly sampled or not, and if not, it shows how to compute its spectrum or its power
Assess the significance of a sinusoidal component in white noise using Fisher's g -statistic. Fisher's g -statistic is the ratio of the largest periodogram value to the sum of all the
There are two design formulas that can help you design FIR filters to meet a set of filter specifications using a Kaiser window. To achieve a sidelobe height of – α dB, the β ( beta ) parameter is
Load a file that contains audio data from a Pacific blue whale, sampled at 4 kHz. The file is from the library of animal vocalizations maintained by the Cornell University Bioacoustics