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Modern scopes tend to use the direct form, though there is much more to an FFT than what you describe.

The next operation is to repair the spectral leakage by using a window function. A Hamming window is a popular one, they all look fairly Gaussian to the untrained eye. Different windows have different tradeoffs in terms of suppression of spectral leakage, widening of the bin bandwidth, and amplitude flatness across the width of a bin. Choice of an appropriate window is often the secret sauce that gives you a usable or useless spectrum.

Take the FFT. This is the standard bit. Square to power. Normalise for bandwidth, and for any input reference levels and gain.

Often at this point, you'll get the option to run a marker across the spectrum, to read out individual frequencies and magnitudes. The simplest (zero effort) marker will convert the bin centre frequency to Hz, which is why you'll get binary frequencies like 23.375Hz when you're expecting some other resolution. The amplitude error for frequencies off the bin centre can often be 1dB for typical windows, to 3dB for a rectangular window (rectangular does have its uses, but not if you don't know what you're doing). A better marker will estimate signal power using the zeroth moment, and signal frequency using the first moment, of the powers of any individual resolved peak across the width of its broadened line, often giving real resolution to 0.001dB and 1/1000th of a bin width.

The marker will usually have a switchable normalisation to either total or per Hz power, and with any luck, referenced to volts or dBm at the front panel.

Modern scopes tend to use the direct form, though there is much more to taking the spectrum than you think.

The next operation is to repair the spectral leakage by using a window function, a Hamming window is a popular one. Different windows have different tradeoffs in terms of suppression of spectral leakage, widening of the bin bandwidth, and amplitude flatness across the width of a bin, but they all look fairly Gaussian to the untrained eye. Choice of an appropriate window is often the secret sauce that gives you a usable or useless spectrum.

Now take the FFT. This is the standard bit. Square to power. Normalise for bandwidth, and for any input reference levels and gain.

Often at this point, you'll get the option to run a marker across the spectrum, to read out individual frequencies and magnitudes. The simplest (zero effort) marker will convert the bin centre frequency to Hz, which is why you'll sometimes get binary frequencies like 23.375Hz when you're expecting some other resolution. The amplitude error for frequencies off the bin centre can often be 1dB for typical windows, to 3dB for a rectangular window (rectangular does have its uses, but only if you know exactly what you're doing). A better marker will estimate signal power using the zeroth moment, and signal frequency using the first moment, of the powers of any individual resolved peak across the width of its broadened line, often giving usable resolution to 0.001dB and 1/1000th of a bin width. If your instrument doesn't give you this, you can post process a raw dump of the spectrum with a spreadsheet or program to get it.

The marker function will usually have a selectable normalisation to either total power or per Hz power, and with any luck, referenced to volts or dBm at the front panel.

If you did want to do the spectrum via an AC, you wouldn't do it directly, multiplying the terms in the input, as the effort involved is O(n^2). You'd use a Fourrier Convolution using O(nlog(n)) effort to compute it. So if you're transforming to do the AC, you might as well just transform to get the spectrum. The AC method was quite popular before the FFT algorithm had been discovered.

If you did want to do the spectrum via an AC, you wouldn't do it directly, multiplying the terms in the input, as the effort involved is O(n^2). You'd use a Fourrier Convolution using O(nlog(n)) effort to compute it. So if you're transforming to do the AC, you might as well just transform to get the spectrum. The AC method was quite popular before the FFT algorithm had been discovered, especially if only a few spectral points were required.

They are slightly different, because they use different portions of the input signal. Let's say we want a 100Hz resolution spectrum, so we transform 10mS of time data. In the direct method, we use 10mS. In the autocorrelation method, we use 20mS, autocorrelate leaving us only the central 10mS as valid data, then transform that. With a stationary signal, the results are very very similar.

Often at this point, you'll get the option to run a marker across the spectrum, to read out individual frequencies and magnitudes. The simplest (zero effort) marker will convert the bin centre frequency to Hz, which is why you'll get binary frequencies like 23.375Hz when you're expecting some other resolution. The amplitude error for frequencies off the bin centre can often be 1dB for typical windows, to 3dB for a rectangular window (rectangular does have its uses, but not if you don't know what you're doing). A better marker will estimate signal power using the zeroth moment, and signal frequency using the first moment, of the powers of any individual resolved peak across the width of its broadened line.

If you did want to do the spectrum via an autocorrelation, you wouldn't do it directly, multiplying the terms in the input, as the effort involved is O(n^2). You'd use a Fourrier Convolution using O(nlog(n)) effort. So if you're transforming to do the convolution, you might as well just transform to get the spectrum.

They are slightly different, because they use different portions of the input signal. Let's say we want a 100Hz resolution spectrum, so we transform 10mS of time data. In the direct method, we use 10mS. In the autocorrelation (AC) method, we use 20mS, autocorrelate leaving us only the central 10mS as valid data, then transform that. With a stationary signal, the results are very very similar.

Often at this point, you'll get the option to run a marker across the spectrum, to read out individual frequencies and magnitudes. The simplest (zero effort) marker will convert the bin centre frequency to Hz, which is why you'll get binary frequencies like 23.375Hz when you're expecting some other resolution. The amplitude error for frequencies off the bin centre can often be 1dB for typical windows, to 3dB for a rectangular window (rectangular does have its uses, but not if you don't know what you're doing). A better marker will estimate signal power using the zeroth moment, and signal frequency using the first moment, of the powers of any individual resolved peak across the width of its broadened line, often giving real resolution to 0.001dB and 1/1000th of a bin width.

If you did want to do the spectrum via an AC, you wouldn't do it directly, multiplying the terms in the input, as the effort involved is O(n^2). You'd use a Fourrier Convolution using O(nlog(n)) effort to compute it. So if you're transforming to do the AC, you might as well just transform to get the spectrum. The AC method was quite popular before the FFT algorithm had been discovered.