need help to understand fourier transfom

Discussion in 'General Electronics Chat' started by vead, Dec 17, 2013.

  1. vead

    Thread Starter Active Member

    Nov 24, 2011
    please anyone help me to understand what does it mean I have read this article but I am bit confused
    A Fourier transform take any function and convert it in to eqquivalent set of sin way If you plot the electrical signal going in to loudspeaker that's playing music you will say wave line where the wave are some time big and some time close together other time smaller other time further Appurt's your ear hear note note vibration and collection of note you hear is the Fourier transform of signal going in to loudspeaker

    can anyone explain with another example what is use of fourier transform in electronics application
  2. tshuck

    Well-Known Member

    Oct 18, 2012
    I'm not quite sure what this example is even trying to say, but a Fourier Transform breaks any periodic signal into a summation of sinusoidal signals.

    For example, a square wave is composed of an infinite number of odd ordered harmonics of the fundamental frequency. So a 10kHz square wave will be, once transformed, a summation of sinusoidal signals at 10kHz, 30kHz, 50kHz, etc.
  3. Veracohr

    Well-Known Member

    Jan 3, 2011
    Have you heard of FFT? It stands for Fast Fourier Transform, and uses the Fourier transform concept to give us nice visual frequency content graphs from signals.
  4. poofjunior

    New Member

    May 21, 2013
    Here's my "in-a-nutshell-lacking-in-mathematical-rigor" explanation.

    Aye the Fourier Transform, is an operation (aka: transformation) performed on another function. In many cases, these functions that get fed into a Fourier Transform are often some form of signal plotted versus time. An audio signal is a great example. The output of a sensor (like an accelerometer) as it changes over time is another example of a signal.

    Before explaining what the Fourier Transform actually does, theres one key thing from math that I need to back myself up. That idea is that any function y = f(x) can be decomposed into an infinite sum of sines waves. In other words, I can take a signal like a square wave, and split it up into an infinite number of separate signals (all sine waves of various frequencies and amplitudes) that, when added together, can completely reproduce that square wave.

    The Fourier Transform does just that; it takes an input signal and splits it into numerous simple sine wave signals with different amplitudes and frequencies.

    There's one more thing that I should mention before things start to come together. What exactly is a sine wave, and why is it special? A sine wave is a simple signal that is, mathematically, very predictable. It has a single frequency and a single amplitude and it repeats itself forever.

    Now, because I can use Fourier Transforms to decompose an input signal into a bunch of sine waves, and because a sine wave is just a single frequency, I can look at my input signal and now know a bit more about the frequency content that makes it up.

    Now let's talk about where this comes into play in the real world.

    Let's say we're listening to rock music, and I want to build up a nice LED necklace that pulses to the beat of the music. With the Fourier Transform, I can do just that! If we sample the audio from the rock band, we can say that the beats from the drums are made of very low-frequency waveforms, compared to the melody and the voice of the singer. If I sample a small window in time and take a look at the frequency content during that time, if I see any strong values in the low-frequency range, I know that a drum beat has just happened. (Thus, I should pulse my LED necklace!)

    There are other applications as well that aren't just in music. In structural analysis, engineers and scientists will strap accelerometers to bridges, introduce a large pulse on the bridge, and see how the bridge vibrates back in response to that pulse. If we sample that accelerometer over time and take the fourier transform of the accel output versus time, we can see that the bridge vibrates in a very distinct way based on which frequencies are stronger from the output of the fourier transform.

    (I hope this helps!)