Projection video display apparatus

1. A projection video display apparatus comprising:

a converter that converts an input video signal having a first number of pixels and a first frame rate (frames per second) into a conversion video signal having a second number of pixels and a second frame rate (frames per second), the second number of pixels being smaller than the first number of pixels, and the second frame rate being an n-th multiple (n is an integer of 2 or greater) of the first frame rate;

a light source;

a light bulb that modulates a light beam emitted from the light source based on the conversion video signal and outputs a video light beam;

an optical element that displaces an optical axis of the video light beam output from the light bulb;

an optical element driving unit that drives the optical element at a frequency F (Hz) based on timing of displaying the conversion video signal, the frequency F being a natural-number multiple of the first frame rate;

a projection optical system that projects the video light beam displaced by the optical element to a projection surface; and

a rotating body that rotates at a rotation speed R (rotations per second),

wherein the rotation speed R is set so as to become a value within a predetermined range corresponding to the frequency F.

2. The projection video display apparatus according to claim 1 , wherein the rotating body is a fan that sends air to at least one of the light source and the light bulb.

3. The projection video display apparatus according to claim 1 , further comprising a controller that sets at least one of the frequency F and the rotation speed R such that the rotation speed R becomes the value within the predetermined range corresponding to the frequency F.

4. The projection video display apparatus according to claim 3 , wherein the controller sets the frequency R such that the following condition is satisfied,

m×F−a<R<m×F+a , or

m×F+b<R <( m+ 1)× F−b,

where R>0, m is an integer of 0 or greater, and 0<a<b<F/2.