Doppler Direction Projection Sign Three-Row Scan - Biophysical Ultrasound: Echo Timing and Acoustic Interfaces Step by Step

Direction controls Doppler sign while projection controls magnitude. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

toward direction gives shift 4

The transmit frequency, flow speed, and sound speed stay fixed. Direction toward with a checked projection gives signed shift 4.

+{2\cdot6\cdot1\cdot1\over3}=4

away direction gives shift -4

The transmit frequency, flow speed, and sound speed stay fixed. Direction away with a checked projection gives signed shift -4.

-{2\cdot6\cdot1\cdot1\over3}=-4

toward direction gives shift 2

The transmit frequency, flow speed, and sound speed stay fixed. Direction toward with a checked projection gives signed shift 2.

+{2\cdot6\cdot1\cdot\frac{1}{2}\over3}=2

Direction changes the sign and projection changes the magnitude

The first two rows flip direction with full projection. The third row points toward the probe but halves the projection, so the shift is positive and smaller.

\begin{array}{c|c|c}\text{direction}&p&\Delta f\\toward&1&4\\away&1&-4\\toward&\frac{1}{2}&2\\\end{array}