From the course: Electronics Foundations: Basic Circuits

Frequency domain

- From a simple sine wave or square wave to the complex signal representing my voice right now, every single signal can be broken down into a collection of sinusoids with different frequencies, amplitudes, and phases. When we view an electrical signal on an oscilloscope, we usually view it as a voltage changing over time. This is called the time domain because it shows how the amplitude of that signal changes over time. This time domain view, amplitude is represented on the vertical axis and time progresses from left to right along the horizontal axis. That signal can be converted from the time domain into another representation called the frequency domain, using a mathematical operator called the Fourier transform, which is named after a French mathematician. The Fourier transform decomposes a time-based signal into the individual frequencies that make it up. When we view a signal in the frequency domain, the vertical axis represents the magnitudes of the individual sinusoids that make up a signal at different frequencies along the horizontal axis. In the case of this simple 60 Hertz sine wave, the frequency domain representation is a single point at 60 Hertz whose magnitude represents the amplitude of that sine wave. Another sine wave, having a higher frequency and a smaller amplitude would appear as a different point in the frequency domain, representing its frequency and amplitude. In addition to amplitude and frequency, each of these sinusoids also has a phase associated with it, which describes how it's shifted in time relative to other sinusoids making up the signal. For this video however, I'm only going to focus on the amplitude and frequency aspects of the sinusoids. If I look at a more complex signal like my voice in the frequency domain, I'll see that it's composed of a huge number of sinusoids, each with a slightly different frequency and amplitude. The plots on the left and right are both showing the exact same signal, they're just showing it in different domains. To wrap my head around the idea that a bunch of sine waves can come together to create complex signals, I think of music and how playing a bunch of different frequencies on my keyboard can come together to build a complex chord. When I play a 440 Hertz sine wave through speakers, it makes a nice peer sounding tone. Playing a 554 Hertz sine wave sounds similar, but with a slightly higher pitch. And a 660 Hertz sine wave is even higher. When I played each of those notes individually, their time domain signals looked like normal sign waves. But when I play all three notes at the same time, those sign waves add together to create something different. I can identify each of the three individual components in the frequency domain. But in the time domain, they're combined to create a completely new signal. It's possible to have a signal like the sine wave shown here that's not centered at zero volts. That occurs when the signal consists of both AC and DC signal components. Looking at the frequency domain, we can see that this signal consists of two parts, a sinusoid at some frequency, and another component at zero Hertz. A sinusoid with a frequency of zero Hertz doesn't oscillate, it remains constant. Which means it's really just a DC voltage. This part of the signal is called the DC offset because it causes the other AC components of the signal to be offset above or below zero volts. The math used in the Fourier transform to convert between the time and frequency domain is complicated and well beyond the scope of this course. Fortunately, if you use any computer-based signal analysis tools, you'll almost certainly find that the Fourier transform has already been implemented for you. The fast Fourier year transform or FFT, is a common processing function that's used to convert signals from the time domain to the frequency domain in software. And the inverse fast Fourier transform or IFFT is its partner function, which converts from the frequency domain back into the time domain.

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