Calculate the missing value in an inverse convolution calculator using original signal, deconvolved signal, and kernel with voltage or time units.
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Inverse Convolution Formula
The calculator uses a scalar inverse convolution relationship between the original signal, the deconvolved signal, and the kernel. Enter any two values to solve for the third.
- O = original signal, in volts (V), millivolts (mV), or microvolts (ฮผV)
- D = deconvolved signal, in volts (V), millivolts (mV), or microvolts (ฮผV)
- K = kernel, in seconds (s), milliseconds (ms), or microseconds (ฮผs)
To calculate the missing value, the formula is rearranged as needed:
- Original signal mode: multiplies the deconvolved signal by the kernel.
- Deconvolved signal mode: divides the original signal by the kernel.
- Kernel mode: divides the original signal by the deconvolved signal.
The calculator first converts entered values to base units, using volts for signal values and seconds for the kernel. After calculating the result, it converts the answer back to the unit selected for the missing field.
Signal and Kernel Unit Conversions
Use these tables to check how values are converted before the formula is applied.
| Signal Unit | Symbol | Equivalent in Volts |
|---|---|---|
| Volt | V | 1 V |
| Millivolt | mV | 0.001 V |
| Microvolt | ฮผV | 0.000001 V |
| Kernel Unit | Symbol | Equivalent in Seconds |
|---|---|---|
| Second | s | 1 s |
| Millisecond | ms | 0.001 s |
| Microsecond | ฮผs | 0.000001 s |
Example Problems
Example 1: Calculate the deconvolved signal
Suppose the original signal is 2 V and the kernel is 0.5 s.
The deconvolved signal is 4 V.
Example 2: Calculate the kernel
Suppose the original signal is 500 mV and the deconvolved signal is 2 V.
First convert 500 mV to volts:
Then divide the original signal by the deconvolved signal:
The kernel is 0.25 s, or 250 ms.
FAQ
Is this the same as full signal deconvolution?
No. Full deconvolution usually works on arrays, sampled signals, Fourier transforms, or filters. This calculator uses a simplified scalar relationship where the original signal equals the deconvolved signal multiplied by a kernel value.
Why does the calculator require exactly two inputs?
The formula has three variables. If you enter exactly two values, the missing value can be solved directly. If you enter only one value, there is not enough information. If you enter all three, there is no missing variable to calculate.
Can any value be zero?
A value used as a divisor cannot be zero. For example, when calculating the deconvolved signal, the kernel cannot be zero because the formula divides by the kernel. When calculating the kernel, the deconvolved signal cannot be zero.
