ConvolutionFlip, shift, multiply, integrate — the graphical method in order.Electrical EngineeringThe overlap region changes as the shift moves, so the answer is piecewise.1Rewrite both in τRename the variable so the shift parameter t is left free to move.2Flip one signalReflect h(τ) about the origin to get h(−τ). Flip the simpler of thetwo.3Shift it by th(t − τ) slides across x(τ) as t runs from far negative to far positive.4Multiply and integrateFor each t, integrate the product across the overlapping regiononly.5Collect the regionsEach new overlap geometry gives a new piece of the finalexpression.Durations add: convolving a 3 ms pulse with a 5 ms response gives an 8ms output. That is a fast sanity check.Convolutionlearnposters.com
Convolution — printable engineering wall chart from LearnPosters. Free vector PDF, US Letter and A4.

Convolution, step by step

The overlap region changes as the shift moves, so the answer is piecewise.

  1. Rewrite both in τRename the variable so the shift parameter t is left free to move.
  2. Flip one signalReflect h(τ) about the origin to get h(−τ). Flip the simpler of the two.
  3. Shift it by th(t − τ) slides across x(τ) as t runs from far negative to far positive.
  4. Multiply and integrateFor each t, integrate the product across the overlapping region only.
  5. Collect the regionsEach new overlap geometry gives a new piece of the final expression.

Durations add: convolving a 3 ms pulse with a 5 ms response gives an 8 ms output. That is a fast sanity check.

Questions about the Convolution poster

What’s on the Convolution poster?
5 numbered steps. The overlap region changes as the shift moves, so the answer is piecewise. Rewrite both in τ — Rename the variable so the shift parameter t is left free to move.; Flip one signal — Reflect h(τ) about the origin to get h(−τ). Flip the simpler of the…; Shift it by t — h(t − τ) slides across x(τ) as t runs from far negative to far positive.; Multiply and integrate — For each t, integrate the product across the overlapping reg…; Collect the regions — Each new overlap geometry gives a new piece of the final expres…. Durations add: convolving a 3 ms pulse with a 5 ms response gives an 8 ms output. That is a fast sanity check.
Who is the Convolution poster for?
Convolution belongs to the Electrical Engineering section rather than to a school year, because engineering is not something one grade owns. Anyone learning signals & systems can pin it up — a beginner, a student mid-course, or someone revising years later.
When should you use the Convolution poster?
Use it whenever an input meets an impulse response and you need the output in time. A wall chart earns its place by being glanceable from where the work is happening, so Convolution belongs on the wall where that engineering work actually happens, within glancing distance, rather than filed away.
What other posters go with Convolution?
Impulse & Step Response, Filter Responses and Bode Plots sit alongside Convolution in the Electrical Engineering section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.Impulse & Step ResponseFilter ResponsesBode Plots
Is the Convolution poster free to download and print?
Yes. Convolution downloads as a free PDF with no account, no email and no watermark, like everything else in the Electrical Engineering section. Print as many copies as you like for a home, a classroom, a library or a tutoring group; reselling the file is the only thing the licence rules out.Read the licence
What size does the Convolution poster print at?
Convolution is a vector PDF laid out for US Letter, and prints on A4 with Fit to page — the same file, no separate download. Because every mark on it is drawn rather than photographed, it stays sharp enlarged to A3, A2 or A1 at a copy shop. Colour carries emphasis only, so a greyscale print of Convolution loses nothing.Printing guide

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