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Tutorials Recently I've been thinking about the process of envelope detection. Tutorial information on this topic is readily available but that information is spread out over a number of DSP textbooks and many Internet web sites.
The purpose of this blog is to summarize various digital envelope detection methods in one place. Here I focus on envelope detection as it is applied to an amplitude-fluctuating sinusoidal signal where the positive-amplitude fluctuations the sinusoid's envelope contain some sort of information.
Let's begin by looking at the simplest envelope detection method. Asynchronous Half-Wave Envelope Detection Figure 1 is a digital version of a popular envelope detector used in the analog world for amplitude modulation AM demodulation in analog AM receivers.
Although the signal waveforms in Figure 1 appear to be continuous, keep in mind that they are indeed discrete-time numerical sequences digital signals. Asynchronous half-wave envelope detector.
Due to the harmonics multiples of the incoming fc carrier frequency generated by half-wave rectification in Figure 1 and possible spectral aliasing depending on the system's fs sample rate, careful spectrum analysis of the half-wave rectified sinusoid is necessary to help you determine the appropriate cutoff frequency of the digital lowpass filter.
Here I used a simple third-order IIR lowpass filter to generate all of the output envelope waveforms presented in this blog. This simple detector is called "asynchronous" because it need not generate a constant amplitude copy of the incoming RF sinusoid, as do some of the other detectors we'll be discussing.
Asynchronous Full-Wave Envelope Detection We can reduce the high-frequency noise riding on the Figure 1 detector output by performing full-wave rectification as shown in Figure 2 .
Asynchronous full-wave envelope detector. Here the lowest-frequency spectral harmonic at the filter's input is 2 fc Hz. So that harmonic is more thoroughly attenuated at the Figure 2 lowpass filter output compared to the first fc Hz harmonic at the Figure 1 filter output.
Asynchronous Real Square-Law Envelope Detection Figure 3 is a digital version of a popular square-law analog envelope detector sometimes called a "product detector". Asynchronous real square-law envelope detector. Here the spectral harmonics at the filter's input are the same as those in Figure 2.
References [2,3] give a mathematical description of the Figure 3 envelope detector. Asynchronous Complex Envelope Detection Figure 4 shows a popular digital envelope detector that uses a Hilbert transformer to compute a complex-valued version of the incoming signal.
This detector is described in more detail in Reference . Asynchronous complex envelope detector. The transformer's passband need only be wide enough to include the spectral energy of the incoming RF signal. This detector is described in more detail in References [2,3].
Asynchronous complex square-law envelope detector. This is a most interesting envelope detector.Return Address on Department of State Envelope Use an actual address (preferably home) where you can be contacted up until your time of departure on the inside of the envelope. If you prefer to use your official "training" email address, see below.
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