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I am using a Canon 450D with 17-85mm Canon lens. I noticed that the image is very noisy when I use my CPL filter. Is my filter bad quality or is this normal? I notice this especially when I take RAW photos.
Image taken at f711, ISO 200, 1/200s, 26mm.
A polarizing filter is not supposed to add noise.
Noise is anything that isn't the correct signal. You didn't specify which of the obviously noisy parts of the image you are asking about. I see several types of noise, some of which could be caused by the filter directly, at least one indirectly, and some not at all.
The first and most obvious noise is the "hazy" appearance. This can be seen especially around the bright cross against the dark background. This could simply be due to a crappy lens, but the filter could also have contributed to it. A picture of the same thing without the filter would have obviously been useful. You may have accidentally smeared something oily on the filter. This could be if you wiped it with a less than clean cloth or tissue, or this cloth or tissue got contaminated, like from sweat or skin oils or sunscreen or whatever.
The general "noisyneess" in the blue sky area looks like mostly sensor noise, but also could be JPG compression artifacts in part. If it is sensor noise and your camera has a decent quality sensor, then this is probably due to underexposure. Check how bright the brightest highlights are. If they aren't near full brightness, then the picture was underexposed. That makes the inherent fixed sensor noise higher relative to the picture signal. The sensor noise is then more obvious after the picture is scaled so that the brightest parts are white, especially in the dark areas.
The filter could have contributed to underexposure because it reduces overall light. If this was not properly compensated for with a longer exposure time or a wider aperture, underexposure would result.
It looks like there could be a little chromatic abberation. This can be seen especially at the edge of the bright dome at the left bottom of the picture. This is because the glass in the lens and the filter has different focusing properties accross the color spectrum. This can be due to a crappy or misaligned lens (again, a picture without the filter would obviously be useful). A bad filter could contribute a little to this, but not much because the light is mostly passing thru it at right angles.
A circular polarizer wouldn't directly create noise. The noise is a function of the sensor and exposure settings. Better filters help capture better images but better filters don't prevent noise.
In this case, underexposure (an effect of the polarizer) may be the reason for noise in that sample image. Additionally, if you're noticing it more when you shoot RAW, that could be because RAW retains more noise than a JPEG that has had in-camera noise reduction already applied. Which is to say: you may be noticing the noise on a RAW image because the RAW file hasn't had any noise reduction applied and the JPEG almost certainly received some in-camera noise reduction.
