MEANFREQ

Purpose:

Computes the mean frequency of the power spectrum of a series.

Syntax:

MEANFREQ(x, fs, frange)

(f, p) = MEANFREQ(x, fs, frange)

Alternate Syntax:

MEANFREQ(Pxx, fs, frange, "psdflag")

(f, p) = MEANFREQ(Pxx, fs, frange, "psdflag")

Returns:

A scalar or array, the mean frequency of the power spectrum over the frequency range.

(f, p) = MEANFREQ(x, fs, range) returns the mean frequency and power over the frequency range.

Example:

W1: gsin(1000, 1/1000, 40) + gsin(1000, 1/1000, 160)

W2: {meanfreq(w1)}

W1 contains a 1000 samples series that is the sum of a 40 Hz sine wave and a 160 Hz sine wave sampled at 1000 Hz.

W2 computes the mean frequency and converts the scalar result to a one point series. The mean frequency is 100 Hz.

Example:

W1: gsin(1000, 1/1000, 40) + gsin(1000, 1/1000, 160)

W2: (f, p) = meanfreq(w1);{f, p};table

W2 == {100, 1}

Same as above, except W2 contains both the mean frequency, 100 Hz and the power, 1.0.

Example:

W1: gsin(1000, 1/1000, 40) + gsin(1000, 1/1000, 160);setvunits("V")

W2: {meanfreq(w1)}

W3: 10*log10(powspec(w1));linedraw(w0, red, w2[1], -inf, w2[1], inf)

Same as the first example, except W3 computes the power spectrum of the series in W1 and a vertical line is drawn at the mean frequency.

Example:

W1: gsin(10000, 1/1000, 100)^3

W2: {meanfreq(w1)}

W3: psd(w1)

W4: {meanfreq(w3, "psd")}

W2 == 120

W4 == 120

W2 computes the mean frequency from the time domain series in W1.

W4 computes the mean frequency from the PSD in W3. The value is identical to W2.

Example:

W1: gsin(10000, 1/1000, 100)^3

W2: {meanfreq(w1)}

W3: powspec(w1)

W4: {meanfreq(w3, "powspec")}

W2 == 120

W4 == 120

Same as above, except W4 computes the mean frequency from the power spectrum in W3.

Example:

W1: gsin(1000, 1/1000, 20)^2

W2: gsin(10000, 1/10000, 100)^2

W3: {meanfreq(W1, {30, 50})}

W4: {meanfreq(W2, {100, 300})}

W5: ravel(w1, w2)

W6: {meanfreq(W5, ravel({30, 50}, {100, 300}))}

W3 == 40

W4 == 200

W6 == {{40, 200}}

W1 and W2 contain two different series with different sample rates.

W3 computes the series power of W1 between 30 Hz and 50 Hz.

W4 computes the series power of W2 between 1000 Hz and 2000 Hz.

W5 combines the data in W1 and W2 into a single two column series.

W6 computes the series power of each column of W5, producing the same result as the individual computations in W3 and W4.

Example:

W1: seedrand(1);gsin(1000, 0.001, 100)^2+gnorm(1000, 0.001)*0.2

W2: psd(w1)

W3: {meanfreq(w1, {150, 300})}

W4: {meanfreq(w2, {150, 300}, "psd")}

W3 == 202.126447

W4 == 202.126447

W1 contains a squared 100 Hz sine wave sampled at 1 kHz with additive normally distributed random noise. The random number generated is set with a seed of 1 for consistent repeated results.

W2 computes the frequency domain PSD of W1.

W3 computes the series power of W1 between 150 Hz and 300 Hz.

W4 computes the series power of W1 between 150 Hz and 300 Hz directly from the PSD in W2.

W3 and W4 produce the same result.

Example:

W1: seedrand(1);gsin(1000, 0.001, 100)^2+gnorm(1000, 0.001)*0.2

W2: powspec(w1)

W3: {meanfreq(w1, rate(w1), {150, 300})}

W4: {meanfreq(w2, xvals(w2), {150, 300}, "powspec")}

W3 == 202.126447

W4 == 202.126447

Same as above, except the sample rate and frequencies are explicit and the input to W4 is the power spectrum in W2.

Remarks:

MEANFREQ computes the average frequency of the energy distribution of the series spectrum. It is the weighted average of the frequencies in the spectrum where the weights are proportional to the power at each frequency.

The input is considered a frequency domain PSD if psdflag is "psd". If psdflag is "powspec", the input is considered a power spectrum as computed by POWSPEC.

See MEDFREQ  to compute the median frequency.

See Also:

BANDPOWER

MEDFREQ

POWSPEC

PSD

XYLOOKUP