A spectrogram is a graph that shows the evolution of the spectrum (the frequency contents) of a signal over time. Often, the frequency is on the vertical axis and time is on the horizontal axis. A spectrogram is computed by “chopping up” the signal into chunks and computing…
After introducing finite-bandwidth square waves in previous articles, I’ll now describe what happens if you follow the naive approach, and just alternate sequences of 1’s and −1’s. As you might expect after reading the previous articles, there are several problems with this. The first problem is that the naive square wave is…
After introducing the finite-bandwidth square wave in a previous article, I’ll show in this one how such a square wave looks in a digital system, so in sampled form. The figure below shows one period of a square wave of 1 kHz, sampled at 44.1 kHz, a widely used…
How would you produce a square wave on a digital system? At first sight, this seems completely trivial. You might think that you could just alternate a series of +1 values with a series of −1 values and be done with it. Well, it doesn’t work like that. An ideal square wave needs infinite bandwith, so creating one is…
After computing The PSF of a Pinhole Camera and showing Some Wacky Pinholes and Their PSF in previous articles, the next step towards ever more realistic PSFs is adding color. A DSLR camera has detector pixels that are sensitive to red, green, and blue, and, since the size of the PSF depends on…
After simulating a round pinhole and showing the resulting point spread function (PSF) both far away (equivalent to the Airy disk) and close by (resulting in a realistic PSF for a DSLR pinhole camera) in The PSF of a Pinhole Camera, I show the PSFs of some more wacky pinholes here…
After introducing the Airy pattern in The Perfect Camera, I will show in this article how the PSF of a pinhole camera looks. A camera with a classical lens focuses the image that would be at infinity on the detector, which means that you actually get (approximately) the Airy pattern as the image of a point source there. This is not true for a pinhole camera, so…
The perfect camera is diffraction limited. This article is written strictly from an optical point of view, so don’t expect a Nikon / Canon / Leica comparison here… Optically, a camera (or telescope or other optical instrument) can be described by its point spread function (PSF), which…
The impulse response of a system is, perhaps not entirely unexpectedly, the response of a system to an impulse. This article introduces this all important concept, and shows how knowing only the impulse response of an LTI system can be used to…
The title of this article is Discrete-Time Signal Processing, although the term digital signal processing (with the abbreviation DSP) is much more common. Both types of signals are discrete in the time dimension, in the sense that they are sequences of numbers. The difference is that a digital signal is…