The wall filter, also known as the high-pass filter, is used in Doppler ultrasound to remove low-frequency signals, which are typically associated with clutter artifacts. Clutter artifacts can be caused by tissue motion or vessel wall movement, and they appear as low-frequency signals that can obscure the desired blood flow signals. By increasing the wall filter setting, these low-frequency signals are filtered out, thus reducing the clutter artifact and providing a clearer depiction of the blood flow.
American Registry for Diagnostic Medical Sonography (ARDMS). Sonography Principles and Instrumentation (SPI) Examination Review Guide.

According to Poiseuille's law, the flow rate of a fluid through a vessel is directly proportional to the fourth power of the vessel's radius. Therefore, a small change in the radius of the vessel has a much larger effect on blood flow compared to changes in pressure gradient, length of the vessel, or viscosity of the fluid.
ARDMS Sonography Principles and Instrumentation guidelines
Poiseuille's law in medical physics and hemodynamics literature.

A high wall filter is used in Doppler ultrasound to eliminate low-frequency signals that may be attributed to vessel wall motion or other low-velocity flows. However, if the wall filter is set too high, it can inadvertently eliminate desired low-frequency Doppler signals that represent real blood flow, particularly in smaller vessels or those with slower flow velocities. This results in a loss of valuable diagnostic information.
References:ARDMS Sonography Principles and Instrumentation (SPI) Review, Doppler Ultrasound section.

Power Doppler, unlike color Doppler, is less angle dependent because it detects the strength of the Doppler signal rather than the velocity of the blood flow. This means it is more sensitive to detecting low-velocity flow and flow in smaller vessels, regardless of the angle between the ultrasound beam and the flow direction. Color Doppler provides information on flow direction and velocity but is highly dependent on the angle of insonation, making it less reliable when the angle is suboptimal.
Reference:
ARDMS Sonography Principles and Instrumentation guidelines
Zwiebel, W. J., & Pellerito, J. S. (2017). Introduction to Vascular Ultrasonography. Elsevier.

Lateral resolution describes the ability of an ultrasound system to distinguish between two structures that are side by side (perpendicular to the path of the ultrasound beam). This type of resolution depends on the beam width; narrower beams provide better lateral resolution. As the ultrasound beam travels deeper into the tissue, it generally widens, which can reduce lateral resolution. Techniques such as focusing the beam can help improve lateral resolution at specific depths by narrowing the beam width.
Reference:
American Registry for Diagnostic Medical Sonography (ARDMS). Sonography Principles and Instrumentation (SPI) Examination Review Guide.