Magnetic Resonance Imaging

Logarithms

If: x = 10^y, then: log(x) = y

If: x = e^y, then: ln(x) = y

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Decibel (dB)

For power levels P₁ and P₂, dB = 10 log(P₁/P₂)

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Exponentials (t is a constant)

y(x) = e^-x/t

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y(x) = (1 - e^-x/t)

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y(x) = (1 - 2e^-x/t)

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Trigonometric Functions and Identities

Sin(q) = Opposite / Hypotenuse
Cos(q) = Adjacent / Hypotenuse
Tan(q) = Opposite / Adjacent

Csc(q) = 1 / Sin(q) = Hypotenuse / Opposite
Sec(q) = 1 / Cos(q) = Hypotenuse / Adjacent
Cot(q) = 1 / Tan(q) = Adjacent / Opposite

Cos(q₁) Cos(q₂) = 1/2 Cos(q₁ - q₂) + 1/2 Cos(q₁ + q₂)
Sin(q₁) Cos(q₂) = 1/2 Sin(q₁ + q₂) + 1/2 Sin(q₁ - q₂)
Sin(q₁) Sin(q₂) = 1/2 Cos(q₁ - q₂) - 1/2 Cos(q₁ + q₂)

sin(x) / x = sinc(x)

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Coordinate Transformation / Roataion Matrix

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Convolution

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